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A081282 Generalized centered polygonal numbers. 4
0, 1, 6, 22, 62, 147, 308, 588, 1044, 1749, 2794, 4290, 6370, 9191, 12936, 17816, 24072, 31977, 41838, 53998, 68838, 86779, 108284, 133860, 164060, 199485, 240786, 288666, 343882, 407247, 479632, 561968, 655248, 760529, 878934, 1011654 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums of A006007.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

a(n) = 2*C(n+3, 5) + C(n+2, 3).

G.f.: x*(1+x^2)/(1-x)^6.

a(n) = n*(n+1)*(n+2)*(n^2+2*n+7)/60. - Carl Najafi, Nov 18 2012

a(0)=0, a(1)=1, a(2)=6, a(3)=22, a(4)=62, a(5)=147, a(n)=6*a(n-1)- 15*a(n-2)+ 20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - Harvey P. Dale, Jan 09 2014

MATHEMATICA

CoefficientList[Series[x (1 + x^2) / (1 - x)^6, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 07 2013 *)

LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 1, 6, 22, 62, 147}, 40] (* Harvey P. Dale, Jan 09 2014 *)

PROG

(MAGMA) [(n*(n+1)*(n+2)*(n^2+2*n+7))/60: n in [0..35]]; // Vincenzo Librandi, Aug 07 2013

CROSSREFS

Cf. A081284.

Sequence in context: A071239 A105450 A011888 * A001769 A166020 A307621

Adjacent sequences:  A081279 A081280 A081281 * A081283 A081284 A081285

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 17 2003

STATUS

approved

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Last modified April 23 18:06 EDT 2019. Contains 322387 sequences. (Running on oeis4.)