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A118277 Generalized 9-gonal numbers. 34
0, 1, 6, 9, 19, 24, 39, 46, 66, 75, 100, 111, 141, 154, 189, 204, 244, 261, 306, 325, 375, 396, 451, 474, 534, 559, 624, 651, 721, 750, 825, 856, 936, 969, 1054, 1089, 1179, 1216, 1311, 1350, 1450, 1491, 1596, 1639, 1749, 1794, 1909, 1956, 2076, 2125, 2250 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums of A195140. - Omar E. Pol, Sep 13 2011

The characteristic function starts 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0 , ... and has the generating function f(x,x^6) in terms of Ramanujan's two-variable theta function. See A080995, A010054, A133100 etc. - Omar E. Pol, Jul 13 2012

Also A179986 and positive terms of A001106 interleaved. - Omar E. Pol, Aug 04 2012

Sequence provides all integers m such that 56*m + 25 is a square. - Bruno Berselli, Oct 07 2015

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

a(n) = n*(7*n-5)/2 for positive and negative n.

a(n) = (1/16)*(14*n^2 + 14*n - 3 + 3*(-1)^n*(2*n + 1)). - R. J. Mathar, Oct 08 2011

G.f.: x*(1+5*x+x^2) / ( (1+x)^2*(1-x)^3 ). - R. J. Mathar, Oct 08 2011

Sum_{n>=1} 1/a(n) = 2*(7 + 5*Pi*tan(3*Pi/14))/25. - Vaclav Kotesovec, Oct 05 2016

E.g.f.: (1/16)*(3*(1 - 2*x)*exp(-x) + (-3 + 28*x + 14*x^2)*exp(x)). - G. C. Greubel, Aug 19 2017

MATHEMATICA

n=9; Union[Table[i((n-2)i-(n-4))/2, {i, -30, 30}]]

LinearRecurrence[{1, 2, -2, -1, 1}, {0, 1, 6, 9, 19}, 60] (* Harvey P. Dale, Jun 08 2016 *)

PROG

(MAGMA) [7*n^2/8+7*n/8-3/16+3*(-1)^n*(1/16+n/8): n in [0..50]]; // Vincenzo Librandi, Oct 10 2011

(PARI) a(n)=7*n*(n+1)/8-3/16+3*(-1)^n*(1+2*n)/16 \\ Charles R Greathouse IV, Jan 18 2012

CROSSREFS

Cf. A001106 (9-gonal numbers).

Column 5 of A195152.

Generalized k-gonal numbers, k>=5: A001318, A000217, A085787, A001082, this sequence, A074377, A195160, A195162, A195313, A195818.

Sequence in context: A078415 A265099 A023041 * A103186 A011988 A161782

Adjacent sequences:  A118274 A118275 A118276 * A118278 A118279 A118280

KEYWORD

nonn,easy

AUTHOR

T. D. Noe, Apr 21 2006

STATUS

approved

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Last modified February 19 11:04 EST 2018. Contains 299330 sequences. (Running on oeis4.)