A082047 Diagonal sums of number array A082046.

1, 2, 7, 24, 69, 170, 371, 736, 1353, 2338, 3839, 6040, 9165, 13482, 19307, 27008, 37009, 49794, 65911, 85976, 110677, 140778, 177123, 220640, 272345, 333346, 404847, 488152, 584669, 695914, 823515, 969216, 1134881, 1322498, 1534183

Offset: 0

Author

Paul Barry, Apr 03 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, A082046, A082107.

Programs

Magma

[(n+1)*(n*(n-1)*(n^2+16)+30)/30: n in [0..40]]; // G. C. Greubel, Dec 24 2022

Mathematica

Table[(n+1)*(n*(n-1)*(n^2+16)+30)/30, {n,0,40}] (* G. C. Greubel, Dec 24 2022 *)
LinearRecurrence[{6,-15,20,-15,6,-1},{1,2,7,24,69,170},40] (* Harvey P. Dale, Jan 25 2024 *)

PARI

a(n) = (n^5+15*n^3+14*n+30)/30; \\ Michel Marcus, Jan 22 2016

SageMath

[(n+1)*(n*(n-1)*(n^2+16)+30)/30 for n in range(41)] # G. C. Greubel, Dec 24 2022

Formula

a(n) = (n^5+15*n^3+14*n+30)/30 = (n+1)*(n^4-n^3+16*n^2-16*n+30)/30.

From G. C. Greubel, Dec 24 2022: (Start)

G.f.: (1 - 4*x + 10*x^2 - 8*x^3 + 5*x^4)/(1-x)^6.

E.g.f.: (1/30)*(30 +30*x +60*x^2 +40*x^3 +10*x^4 +x^5)*exp(x). (End)