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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 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 January 23 06:15 EST 2019. Contains 319374 sequences. (Running on oeis4.)