A082114 Diagonal sums of number array A082110.

1, 2, 9, 32, 89, 210, 441, 848, 1521, 2578, 4169, 6480, 9737, 14210, 20217, 28128, 38369, 51426, 67849, 88256, 113337, 143858, 180665, 224688, 276945, 338546, 410697, 494704, 591977, 704034, 832505, 979136, 1145793, 1334466, 1547273

Offset

0,2

Links

G. C. Greubel, 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) = (n+1)*(n^4 - n^3 + 26*n^2 - 26*n + 30)/30.

From G. C. Greubel, Dec 22 2022: (Start)

G.f.: (1 - 4*x + 12*x^2 - 12*x^3 + 7*x^4)/(1-x)^6.

E.g.f.: (1/30)*(30 + 30*x + 90*x^2 + 50*x^3 + 10*x^4 + x^5)*exp(x). (End)

Mathematica

LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 2, 9, 32, 89, 210}, 51] (* G. C. Greubel, Dec 22 2022 *)

Prog

(Magma) [(n+1)*(n^4-n^3+26*n^2-26*n+30)/30: n in [0..50]]; // G. C. Greubel, Dec 22 2022
(SageMath) [(n+1)*(n^4-n^3+26*n^2-26*n+30)/30 for n in range(51)] # G. C. Greubel, Dec 22 2022

Crossrefs

Cf. A082045, A082107, A082110.

Sequence in context: A109770 A242512 A198016 * A332870 A074084 A053152

Adjacent sequences: A082111 A082112 A082113 * A082115 A082116 A082117

Keyword

easy,nonn

Author

Paul Barry, Apr 04 2003

Status

approved