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A195313 Generalized 13-gonal numbers: n*(11*n-9)/2, n=0,1,-1,2,-2,... 27
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also generalized tridecagonal numbers or generalized triskaidecagonal numbers.

Also A211013 and positive terms of A051865 interleaved. - Omar E. Pol, Aug 04 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

FORMULA

Contribution by Bruno Berselli, Sep 15 2011: (Start)

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.

a(n)-a(n-2) = A175885(n). (End)

Sum_{n>=1} 1/a(n) = 22/81 + 2*Pi*cot(2*Pi/11)/9. - Vaclav Kotesovec, Oct 05 2016

MATHEMATICA

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 *)

PROG

(MAGMA) [(22*n*(n+1)+7*(2*n+1)*(-1)^n-7)/16: n in [0..50]]; // Vincenzo Librandi, Sep 16 2011

(MAGMA) A195313:=func<n | n*(11*n-9)/2>; [0] cat [A195313(n*m): m in [1, -1], n in [1..25]]; // Bruno Berselli, Nov 13 2012

(PARI) a(n)=(22*n*(n+1)+7*(2*n+1)*(-1)^n-7)/16 \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Partial sums of A195312. Column 9 of A195152.

Generalized k-gonal numbers, k>=5: A001318, (A000217)A085787, A001082, A118277, A074377, A195160, A195162, this sequence, A195818.

Sequence in context: A220045 A101215 A102249 * A219829 A062370 A069960

Adjacent sequences:  A195310 A195311 A195312 * A195314 A195315 A195316

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Sep 14 2011

STATUS

approved

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Last modified February 17 23:47 EST 2018. Contains 299297 sequences. (Running on oeis4.)