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A271870 Convolution of nonzero hexagonal numbers (A000384) with themselves. 4
1, 12, 66, 236, 651, 1512, 3108, 5832, 10197, 16852, 26598, 40404, 59423, 85008, 118728, 162384, 218025, 287964, 374794, 481404, 610995, 767096, 953580, 1174680, 1435005, 1739556, 2093742, 2503396, 2974791, 3514656, 4130192, 4829088, 5619537, 6510252, 7510482, 863002888 (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, Hexagonal Number

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

FORMULA

O.g.f.: (1 + 3*x)^2/(1 - x)^6.

E.g.f.: (30 + 330*x + 645*x^2 + 365*x^3 + 70*x^4 + 4*x^5)*exp(x)/30.

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)*(4*n^2 + 6*n + 5)/30.

MAPLE

A271870:=n->(n+1)*(n+2)*(n+3)*(4*n^2+6*n+5)/30: seq(A271870(n), n=0..50); # Wesley Ivan Hurt, Apr 20 2016

MATHEMATICA

LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 12, 66, 236, 651, 1512}, 36]

Table[(n + 1) (n + 2) (n + 3) ((4 n^2 + 6 n + 5)/30), {n, 0, 35}]

PROG

(MAGMA) [(n+1)*(n+2)*(n+3)*(4*n^2+6*n+5)/30 : n in [0..40]]; // Wesley Ivan Hurt, Apr 20 2016

(PARI) a(n)=binomial(n+3, 3)*(4*n^2 + 6*n + 5)/5 \\ Charles R Greathouse IV, Jul 26 2016

CROSSREFS

Cf. A000384.

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

Sequence in context: A014787 A007249 A112142 * A114243 A000972 A180392

Adjacent sequences:  A271867 A271868 A271869 * A271871 A271872 A271873

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Apr 20 2016

STATUS

approved

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Last modified October 16 00:50 EDT 2018. Contains 316252 sequences. (Running on oeis4.)