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A272103 Convolution of nonzero heptagonal numbers (A000566) with themselves. 0
1, 14, 85, 320, 910, 2156, 4494, 8520, 15015, 24970, 39611, 60424, 89180, 127960, 179180, 245616, 330429, 437190, 569905, 733040, 931546, 1170884, 1457050, 1796600, 2196675, 2665026, 3210039, 3840760, 4566920, 5398960, 6348056, 7426144, 8645945, 10020990, 11565645, 13295136 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..35.

OEIS Wiki, Figurate numbers

Eric Weisstein's World of Mathematics, Heptagonal Number

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

FORMULA

O.g.f.: (1 + 4*x)^2/(1 - x)^6.

E.g.f.: (24 + 312*x + 696*x^2 + 424*x^3 + 85*x^4 + 5*x^5)*exp(x)/24.

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).

a(n) = (n + 1)*(n + 2)*(n + 3)*(5*n^2 + 5*n + 4)/24.

MATHEMATICA

LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 14, 85, 320, 910, 2156}, 36]

Table[(n + 1) (n + 2) (n + 3) ((5 n^2 + 5 n + 4)/24), {n, 0, 35}]

CROSSREFS

Cf. A000566.

Cf. similar sequences of the convolution of k-gonal numbers with themselves listed in A271662.

Sequence in context: A273182 A341854 A025607 * A244865 A059600 A206621

Adjacent sequences: A272100 A272101 A272102 * A272104 A272105 A272106

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Apr 20 2016

STATUS

approved

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Last modified November 29 18:13 EST 2022. Contains 358431 sequences. (Running on oeis4.)