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A195160 Generalized 11-gonal numbers. 28
0, 1, 8, 11, 25, 30, 51, 58, 86, 95, 130, 141, 183, 196, 245, 260, 316, 333, 396, 415, 485, 506, 583, 606, 690, 715, 806, 833, 931, 960, 1065, 1096, 1208, 1241, 1360, 1395, 1521, 1558, 1691, 1730, 1870, 1911, 2058, 2101, 2255, 2300, 2461, 2508, 2676 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also generalized hendecagonal numbers.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

FORMULA

n*(9*n-7)/2 for n = 0,1,-1,2,-2,3,-3,4,-4,..

From Bruno Berselli, Sep 14 2011: (Start)

G.f.: x*(1+7*x+x^2)/((1+x)^2*(1-x)^3).

a(n) = (18*n*(n+1)+5*(2*n+1)*(-1)^n-5)/16.

a(2n) = A062728(n), a(2n-1) = A051682(n). (End)

Sum_{n>=1} 1/a(n) = 18/49 + 2*Pi*cot(2*Pi/9)/7. - Vaclav Kotesovec, Oct 05 2016

MATHEMATICA

CoefficientList[Series[x (1 + 7 x + x^2)/((1 + x)^2 (1 - x)^3), {x, 0, 60}], x] (* Vincenzo Librandi, Apr 09 2013 *)

PROG

(MAGMA) I:=[0, 1, 8, 11, 25]; [n le 5 select I[n] else Self(n-1)+2*Self(n-2)-2*Self(n-3)-Self(n-4)+Self(n-5): n in [1..50]]; // Vincenzo Librandi, Apr 09 2013

(PARI) a(n)=(18*n*(n+1)+5*(2*n+1)*(-1)^n-5)/16 \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Partial sums of A195159. Column 7 of A195152.

Generalized k-gonal numbers, k>=5: A001318, A000217, A085787, A001082, A118277, A074377, this sequence, A195162, A195313, A195818.

Sequence in context: A243520 A129730 A291664 * A053701 A029615 A051791

Adjacent sequences:  A195157 A195158 A195159 * A195161 A195162 A195163

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Sep 10 2011

STATUS

approved

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Last modified February 19 09:11 EST 2018. Contains 299330 sequences. (Running on oeis4.)