|
|
A015577
|
|
a(n+1) = 8*a(n) + 9*a(n-1), a(0) = 0, a(1) = 1.
|
|
9
|
|
|
0, 1, 8, 73, 656, 5905, 53144, 478297, 4304672, 38742049, 348678440, 3138105961, 28242953648, 254186582833, 2287679245496, 20589113209465, 185302018885184, 1667718169966657, 15009463529699912, 135085171767299209, 1215766545905692880, 10941898913151235921
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Number of walks of length n between any two distinct nodes of the complete graph K_10. Example: a(2) = 8 because the walks of length 2 between the nodes A and B of the complete graph ABCDEFGHIJ are: ACB, ADB, AEB, AFB, AGB, AHB, AIB and AJB. - Emeric Deutsch, Apr 01 2004
The ratio a(n+1)/a(n) converges to 9 as n approaches infinity. - Felix P. Muga II, Mar 09 2014
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x/((1+x)*(1-9*x)).
E.g.f. exp(4*x)*sinh(5*x)/5.
a(n) = (9^n - (-1)^n)/10. (End)
|
|
MAPLE
|
|
|
MATHEMATICA
|
Table[(9^n - (-1)^n)/10, {n, 0, 30}] (* or *) LinearRecurrence[{8, 9}, {0, 1}, 30] (* G. C. Greubel, Jan 06 2018 *)
|
|
PROG
|
(PARI) A015577_vec(N=20)=Vec(O(x^N)+1/(1-8*x-9*x^2), -N-1) \\ M. F. Hasler, Jun 14 2008, edited Oct 25 2019
(PARI) for(n=0, 30, print1((9^n - (-1)^n)/10, ", ")) \\ G. C. Greubel, Jan 06 2018
(Sage) [lucas_number1(n, 8, -9) for n in range(0, 19)] # Zerinvary Lajos, Apr 25 2009
(Maxima)
a[0]:0$
a[n]:=9^(n-1)-a[n-1]$
|
|
CROSSREFS
|
Cf. A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501, A015552, A093134, A015565. - Vladimir Joseph Stephan Orlovsky, Dec 11 2008
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|