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Search: a036987 -id:a036987
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A154402 Inverse Moebius transform of Fredholm-Rueppel sequence, cf. A036987. +20
43
1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2, 2, 1, 3, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 3, 1, 1, 3, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 3, 1, 2, 4, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 3, 1, 2, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 3, 2, 1, 3, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Number of ways to write n as a sum a_1 + ... + a_k where the a_i are positive integers and a_i = 2 * a_{i-1}, cf. A000929.
Number of divisors of n of the form 2^k - 1 (A000225) for k >= 1. - Jeffrey Shallit, Jan 23 2017
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537 (first 10000 terms from Robert Israel)
FORMULA
G.f.: Sum_{k>0} x^(2^k-1)/(1-x^(2^k-1)).
From Antti Karttunen, Jun 11 2018: (Start)
a(n) = Sum_{d|n} A036987(d).
a(n) = A305426(n) + A036987(n). (End)
a(n) = A147645(n) + A353786(n). - Antti Karttunen, May 12 2022
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A065442 = 1.606695... . - Amiram Eldar, Dec 31 2023
MAPLE
N:= 200: # to get a(1)..a(N)
A:= Vector(N):
for k from 1 do
t:= 2^k-1;
if t > N then break fi;
R:= [seq(i, i=t..N, t)];
A[R]:= map(`+`, A[R], 1)
od:
convert(A, list); # Robert Israel, Jan 23 2017
MATHEMATICA
Table[DivisorSum[n, 1 &, IntegerQ@ Log2[# + 1] &], {n, 105}] (* Michael De Vlieger, Jun 11 2018 *)
PROG
(PARI)
A209229(n) = (n && !bitand(n, n-1));
A036987(n) = A209229(1+n);
A154402(n) = sumdiv(n, d, A036987(d)); \\ Antti Karttunen, Jun 11 2018
(PARI) A154402(n) = { my(m=1, s=0); while(m<=n, s += !(n%m); m += (m+1)); (s); }; \\ Antti Karttunen, May 12 2022
CROSSREFS
Cf. A000225, A000929, A001511, A036987, A065442, A147645, A161790 (positions of 1's), A305426, A353786.
Cf. also A305436.
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Jan 08 2009
STATUS
approved
A135416 a(n) = A036987(n)*(n+1)/2. +20
31
1, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Guy Steele defines a family of 36 integer sequences, denoted here by GS(i,j) for 1 <= i, j <= 6, as follows. a[1]=1; a[2n] = i-th term of {0,1,a[n],a[n]+1,2a[n],2a[n]+1}; a[2n+1] = j-th term of {0,1,a[n],a[n]+1,2a[n],2a[n]+1}. The present sequence is GS(1,5).
The full list of 36 sequences:
GS(1,1) = A000007
GS(1,2) = A000035
GS(1,3) = A036987
GS(1,4) = A007814
GS(1,5) = A135416 (the present sequence)
GS(1,6) = A135481
GS(2,1) = A135528
GS(2,2) = A000012
GS(2,3) = A000012
GS(2,4) = A091090
GS(2,5) = A135517
GS(2,6) = A135521
GS(3,1) = A036987
GS(3,2) = A000012
GS(3,3) = A000012
GS(3,4) = A000120
GS(3,5) = A048896
GS(3,6) = A038573
GS(4,1) = A135523
GS(4,2) = A001511
GS(4,3) = A008687
GS(4,4) = A070939
GS(4,5) = A135529
GS(4,6) = A135533
GS(5,1) = A048298
GS(5,2) = A006519
GS(5,3) = A080100
GS(5,4) = A087808
GS(5,5) = A053644
GS(5,6) = A000027
GS(6,1) = A135534
GS(6,2) = A038712
GS(6,3) = A135540
GS(6,4) = A135542
GS(6,5) = A054429
GS(6,6) = A003817
(with a(0)=1): Moebius transform of A038712.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to binary expansion of n
FORMULA
G.f.: sum{k>=1, 2^(k-1)*x^(2^k-1) }.
Recurrence: a(2n+1) = 2a(n), a(2n) = 0, starting a(1) = 1.
MAPLE
GS:=proc(i, j, M) local a, n; a:=array(1..2*M+1); a[1]:=1;
for n from 1 to M do
a[2*n] :=[0, 1, a[n], a[n]+1, 2*a[n], 2*a[n]+1][i];
a[2*n+1]:=[0, 1, a[n], a[n]+1, 2*a[n], 2*a[n]+1][j];
od: a:=convert(a, list); RETURN(a); end;
GS(1, 5, 200):
MATHEMATICA
i = 1; j = 5; Clear[a]; a[1] = 1; a[n_?EvenQ] := a[n] = {0, 1, a[n/2], a[n/2]+1, 2*a[n/2], 2*a[n/2]+1}[[i]]; a[n_?OddQ] := a[n] = {0, 1, a[(n-1)/2], a[(n-1)/2]+1, 2*a[(n-1)/2], 2*a[(n-1)/2]+1}[[j]]; Array[a, 105] (* Jean-François Alcover, Sep 12 2013 *)
PROG
(PARI)
A048298(n) = if(!n, 0, if(!bitand(n, n-1), n, 0));
A135416(n) = (A048298(n+1)/2); \\ Antti Karttunen, Jul 22 2018
(Python)
def A135416(n): return int(not(n&(n+1)))*(n+1)>>1 # Chai Wah Wu, Jul 06 2022
CROSSREFS
Equals A048298(n+1)/2. Cf. A036987, A182660.
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, based on a message from Guy Steele and Don Knuth, Mar 01 2008
EXTENSIONS
Formulae and comments by Ralf Stephan, Jun 20 2014
STATUS
approved
A135560 a(n) = A007814(n) + A036987(n-1) + 1. +20
6
2, 3, 1, 4, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 6, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 7, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 8, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 6, 1, 2, 1, 3, 1, 2, 1, 4, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
FORMULA
a(2^k) = k+2; a(2^k + 2^(k-1)) = k. - Reinhard Zumkeller, Mar 02 2008
MATHEMATICA
a[n_] := 1 + IntegerExponent[n, 2] + Sum[(-1)^(n - k - 1)*Binomial[n - 1, k]* Sum[Binomial[k, 2^j - 1], {j, 0, k}], {k, 0, n - 1}]; Table[a[n], {n, 1, 25}] (* G. C. Greubel, Oct 17 2016 *)
PROG
(PARI) a(n)=my(t=valuation(n, 2)); t + (n==2^t) + 1 \\ Charles R Greathouse IV, Oct 17 2016
(Python)
def A135560(n): return (m:=(~n & n-1)).bit_length()+int(m==n-1)+1 # Chai Wah Wu, Jul 06 2022
CROSSREFS
Cf. A007814, A036987, A091090, A135534, A135561.
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 01 2008
EXTENSIONS
More terms from Reinhard Zumkeller, Mar 02 2008
STATUS
approved
A265754 Reduced frequency counts for A004001: a(n) = A265332(n+1) - A036987(n). +20
6
1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 2, 1, 2, 3, 4, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 5, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Can be generated recursively by first setting R_1 = (1), after which each R_n is obtained by replacing in R_{n-1} each term k with terms 1 .. k, followed by final n. This sequence is then obtained by concatenating all levels R_1, R_2, ..., R_inf together. See page 230 in Kubo-Vakil paper (page 6 in PDF).
Deleting all 1's and decrementing the remaining terms by one gives the sequence back.
Comment from N. J. A. Sloane, Nov 05 2017: (Start)
The following simple Pascal-like triangle produces the same sequence. Construct a triangle T(n,k) of strings (with 0 <= k <= n), where T(0,0) = {1}, T(n,n) = {n+1}, and otherwise T(n,k) is the concatenation of T(n-1,k-1) and T(n-1,k). The first few rows of the triangle (where the strings T(n,k) are shown without spaces for legibility) are:
1
1,2
1,12,3
1,112,123,4
1,1112,112123,1234,5
1,11112,1112112123,1121231234,12345,6
...
Now read the strings across the rows to get the sequence. T(n,k) has length binomial(n,k). (End)
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..8191
T. Kubo and R. Vakil, On Conway's recursive sequence, Discr. Math. 152 (1996), 225-252.
FORMULA
a(n) = A265332(n+1) - A036987(n).
As a recurrence: If A036987(n) = 1 [when n is of the form 2^k -1], a(n) = A070939(n), else if a(n+1) = 1, a(n) = a(2^A000523(n) - A266349(n)), otherwise a(n) = a(n+1)-1.
Other identities. For all n >= 1:
a(n) = A266640(A054429(n)).
a(A000225(n)) = n.
EXAMPLE
Illustration of the sequence as a tree:
1
/ \
1 2
/ /|\
1 1 2 3_________
/ / /| | \ \ \
1 1 1 2 1 2 3__ 4________
/ / / /| | / \ |\ \ \ \ \ \ \
1 1 1 1 2 1 1 2 1 2 3 1 2 3 4 5
etc.
Compare with the illustration in A265332.
PROG
(Scheme, two variants)
(define (A265754 n) (- (A265332 (+ 1 n)) (A036987 n)))
(definec (A265754 n) (cond ((= 1 (A036987 n)) (A070939 n)) ((> (A265754 (+ 1 n)) 1) (- (A265754 (+ 1 n)) 1)) (else (A265754 (- (A000079 (A000523 n)) (A266349 n))))))
CROSSREFS
Cf. A004001, A036987, A054429, A070939, A265332, A266348, A266349.
Cf. A000225 (positions of records, where n appears first time).
Cf. A266640 (obtained from the mirror image of the same tree).
See A293959 for another version.
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 10 2016
STATUS
approved
A127802 a(0) = 1, a(n) = 3*A036987(n), n>1. +20
3
1, 3, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Row sums of number triangle A127801.
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..16384
PROG
(Python)
def A127802(n): return 3*int(not(n&(n+1))) if n else 1 # Chai Wah Wu, Jul 06 2022
CROSSREFS
Cf. A036987, A043529.
KEYWORD
nonn
AUTHOR
Paul Barry, Jan 29 2007
STATUS
approved
A130093 A051731 * a lower triangular matrix with A036987 on the main diagonal and the rest zeros. +20
3
1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Right border = A036987, the Fredholm-Rueppel sequence, (1, 1, 0, 1, 0, 0, 0, 1, 0, ...). Row sums = the ruler function, A001511: (1, 2, 1, 3, 1, 2, 1, 4, ...).
A130093 also = A047999 (Sierpinski's gasket) * A036987 diagonalized, as infinite lower triangular matrices. - Gary W. Adamson, Oct 21 2009
Eigensequence of A130093 = A001511, (same sequence as row sums). - Gary W. Adamson, Oct 21 2009
Equals Sierpinski's gasket, A047999 * A036987 (diagonalized); as infinite lower triangular matrices. - Gary W. Adamson, Oct 26 2009
LINKS
Table of n, a(n) for n=1..55.
FORMULA
Inverse Moebius transform of a lower triangular matrix with A036987 (the Fredholm-Rueppel sequence) on the main diagonal and the rest zeros.
EXAMPLE
First few rows of the triangle are:
1;
1, 1;
1, 0, 0;
1, 1, 0, 1;
1, 0, 0, 0, 0;
1, 1, 0, 0, 0, 0;
1, 0, 0, 0, 0, 0, 0;
1, 1, 0, 1, 0, 0, 0, 1;
...
CROSSREFS
Cf. A001511, A051731, A036987.
Cf. A047999. - Gary W. Adamson, Oct 21 2009, Oct 26 2009
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, May 06 2007
STATUS
approved
A266341 If A036987(n) = 1, a(n) = n - A053644(n), otherwise a(n) = n - A053644(n) + 2^(A063250(n)-1). +20
3
0, 0, 1, 1, 2, 3, 3, 3, 4, 5, 6, 7, 6, 7, 7, 7, 8, 9, 10, 11, 12, 13, 14, 15, 12, 13, 14, 15, 14, 15, 15, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 24, 25, 26, 27, 28, 29, 30, 31, 28, 29, 30, 31, 30, 31, 31, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Informally: In binary representation of n, move the most significant 1-bit to the position of the most significant 0-bit ("the leftmost free hole"), and remove it altogether if there are no such holes, i.e., if n is one of the terms of A000225. When the subsets of nonnegative integers are associated with the binary expansion of n in the usual way (bit-k is 1 if number k is present in the set, and 0 stands for an empty set) then a(n) corresponds to the set obtained by "squashing" the set which corresponds to n. See Kubo & Vakil paper, page 240, 8.1 Compression revisited.
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..8191
T. Kubo and R. Vakil, On Conway's recursive sequence, Discr. Math. 152 (1996), 225-252.
FORMULA
a(0) = 0; after which, for n = 2^k - 1 (when k >= 1) a(n) = 2^(k-1) - 1, otherwise a(n) = n - A053644(n) + 2^(A063250(n)-1).
Equally: if A063250(n) = 0, a(n) = n - A053644(n), otherwise a(n) = n - A053644(n) + 2^(A063250(n)-1).
Other identities. For all n >= 0:
a(n) = A209862(-1+A004001(1+A209861(n))). [Not yet proved that the required permutations are just A209861 & A209862, although this has been checked empirically up to n=32769. See also Kubo & Vakil paper.]
EXAMPLE
For n=13, "1101" in binary, we remove the most significant bit to get "101", where the most significant nonleading 0 is then filled with that 1, to get "111", which is 7's binary representation, thus a(13) = 7.
For n=15, "1111" in binary, we remove the most significant bit to get "111" (= 7), and as there is no most significant nonleading 0 present, the result is just that, and a(15) = 7.
For n=21, "10101" in binary, removing the most significant bit and moving it to the position of next zero results "1101", thus a(21) = 13.
PROG
(define (A266341 n) (+ (- n (A053644 n)) (if (zero? (A063250 n)) 0 (A000079 (- (A063250 n) 1)))))
(Python)
from sympy import catalan
def a063250(n):
if n<2: return 0
b=bin(n)[2:]
s=0
while b.count("0")!=0:
N=int(b[-1] + b[:-1], 2)
s+=1
b=bin(N)[2:]
return s
def a053644(n): return 0 if n==0 else 2**(len(bin(n)[2:]) - 1)
def a036987(n): return catalan(n)%2
def a(n): return n - a053644(n) if a036987(n)==1 else n - a053644(n) + 2**(a063250(n) - 1) # Indranil Ghosh, May 25 2017
(PARI) a(n) = my(s=bitnegimply(n>>1, n)); n - if(n, 1<<logint(n, 2)) + if(s, 1<<logint(s, 2)); \\ Kevin Ryde, Jun 15 2023
CROSSREFS
Cf. A000079, A000225, A036987, A053644, A063250.
Cf. also A004001, A209861, A209862.
KEYWORD
nonn,easy
AUTHOR
Antti Karttunen, Jan 13 2016
STATUS
approved
A115367 Row sums of correlation triangle for Fredholm-Rueppel sequence A036987. +20
1
1, 2, 2, 4, 4, 4, 5, 6, 7, 6, 9, 6, 9, 6, 10, 8, 12, 8, 14, 8, 14, 8, 16, 8, 16, 8, 16, 8, 16, 8, 17, 10, 19, 10, 21, 10, 21, 10, 23 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
If a sequence has g.f. A(x), its correlation triangle has g.f. A(x)A(x*y)/(1-x^2*y). (Observation due to Christian G. Bower).
LINKS
Table of n, a(n) for n=0..38.
FORMULA
G.f. : (sum{k>=0, x^(2k-1)})^2/(1-x^2); a(n)=sum{k=0..n, sum{j=0..k, A036987(j)}*sum{j=0..n-k, A036987(j)*(-1)^(n-k-j)}}.
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jan 21 2006
STATUS
approved
A115381 Correlation triangle for Fredholm-Rueppel sequence A036987. +20
0
1, 1, 1, 0, 2, 0, 1, 1, 1, 1, 0, 1, 2, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 3, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 3, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 3, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 3, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Row sums are A115367. T(2n,n) is partial sums of squares of A036987(n).
LINKS
Table of n, a(n) for n=0..104.
FORMULA
G.f.: A(x)A(x*y)/(1-x^2*y) where A(x)=sum{k>=0, x^(2^k-1)}. Number triangle T(n, k)=sum{j=0..n, if(j<=k, A036987(k-j), 0)*if(j<=(n-k), A036987(n-k-j), 0)}
EXAMPLE
Triangle begins
1,
1, 1,
0, 2, 0,
1, 1, 1, 1,
0, 1, 2, 1, 0,
0, 1, 1, 1, 1, 0,
0, 0, 1, 3, 1, 0, 0,
1, 0, 1, 1, 1, 1, 0, 1,
0, 1, 0, 1, 3, 1, 0, 1, 0,
0, 1, 0, 1, 1, 1, 1, 0, 1, 0,
0, 0, 1, 1, 1, 3, 1, 1, 1, 0, 0,
0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0,
0, 0, 0, 1, 1, 1, 3, 1, 1, 1, 0, 0, 0,
0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0,
0, 0, 0, 0, 1, 1, 1, 4, 1, 1, 1, 0, 0, 0, 0,
1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1,
0, 1, 0, 0, 0, 1, 1, 1, 4, 1, 1, 1, 0, 0, 0, 1, 0
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Jan 21 2006
STATUS
approved
A127822 Triangle whose row sums modulo 2 give the Fredholm-Rueppel sequence A036987. +20
0
1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Row sums are A111982. Unsigned version of A111967.
LINKS
Table of n, a(n) for n=0..83.
FORMULA
G.f. of k-th column is x^k*if(k=0,1,x*sum{j=0..\infty, x^(-2^(j/2)*(((k+2)/(2*sqrt(2))-(k+1))(-1)^j-(k+2)/(2*sqrt(2))-(k+1))-(k+2))+1+x}
EXAMPLE
Triangle begins
1,
0, 1,
0, 1, 1,
0, 1, 1, 1,
0, 0, 0, 1, 1,
0, 1, 1, 0, 1, 1,
0, 0, 0, 0, 0, 1, 1,
0, 1, 1, 1, 0, 0, 1, 1,
0, 0, 0, 0, 0, 0, 0, 1, 1,
0, 0, 0, 1, 1, 0, 0, 0, 1, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1,
0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Jan 30 2007
STATUS
approved
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Last modified September 16 08:55 EDT 2024. Contains 375959 sequences. (Running on oeis4.)