A272103 Convolution of nonzero heptagonal numbers (A000566) with themselves.

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

Offset: 0

Author

Ilya Gutkovskiy, Apr 20 2016

Keywords

• nonn
• easy

Links

• 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)

Crossrefs

Cf. A000566.

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

Programs

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}]

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.