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

Author

Paul Barry, Apr 04 2003

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A082045, A082107, A082110.

Programs

Magma

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

Mathematica

LinearRecurrence[{6,-15,20,-15,6,-1}, {1,2,9,32,89,210}, 51] (* 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

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)