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A195313
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Generalized 13-gonal numbers: m*(11*m-9)/2 with m = 0, 1, -1, 2, -2, 3, -3, ...
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46
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0, 1, 10, 13, 31, 36, 63, 70, 106, 115, 160, 171, 225, 238, 301, 316, 388, 405, 486, 505, 595, 616, 715, 738, 846, 871, 988, 1015, 1141, 1170, 1305, 1336, 1480, 1513, 1666, 1701, 1863, 1900, 2071, 2110, 2290, 2331, 2520, 2563, 2761, 2806, 3013, 3060, 3276
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OFFSET
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0,3
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COMMENTS
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Also generalized tridecagonal numbers or generalized triskaidecagonal numbers.
Numbers k for which 88*k + 81 is a square. - Bruno Berselli, Jul 10 2018
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LINKS
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FORMULA
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G.f.: x*(1 + 9*x + x^2)/((1 + x)^2*(1 - x)^3).
a(n) = (22*n*(n + 1) + 7*(2*n + 1)*(-1)^n - 7)/16.
Sum_{n>=1} 1/a(n) = 22/81 + 2*Pi*cot(2*Pi/11)/9. - Vaclav Kotesovec, Oct 05 2016
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MAPLE
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a:= n-> (m-> m*(11*m-9)/2)(-ceil(n/2)*(-1)^n):
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MATHEMATICA
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lim = 50; Sort[Table[n*(11*n - 9)/2, {n, -lim, lim}]] (* T. D. Noe, Sep 15 2011 *)
Accumulate[With[{nn=30}, Riffle[9Range[0, nn], Range[1, 2nn+1, 2]]]] (* Harvey P. Dale, Sep 24 2011 *)
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PROG
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(Magma) [(22*n*(n+1)+7*(2*n+1)*(-1)^n-7)/16: n in [0..50]]; // Vincenzo Librandi, Sep 16 2011
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CROSSREFS
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Sequences of generalized k-gonal numbers: A001318 (k=5), A000217 (k=6), A085787 (k=7), A001082 (k=8), A118277 (k=9), A074377 (k=10), A195160 (k=11), A195162 (k=12), this sequence (k=13), A195818 (k=14), A277082 (k=15), A274978 (k=16), A303305 (k=17), A274979 (k=18), A303813 (k=19), A218864 (k=20), A303298 (k=21), A303299 (k=22), A303303 (k=23), A303814 (k=24), A303304 (k=25), A316724 (k=26), A316725 (k=27), A303812 (k=28), A303815 (k=29), A316729 (k=30).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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