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

0,2

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^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)

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 *)

Prog

(PARI) a(n) = (n^5+15*n^3+14*n+30)/30; \\ Michel Marcus, Jan 22 2016
(Magma) [(n+1)*(n*(n-1)*(n^2+16)+30)/30: n in [0..40]]; // G. C. Greubel, Dec 24 2022
(SageMath) [(n+1)*(n*(n-1)*(n^2+16)+30)/30 for n in range(41)] # G. C. Greubel, Dec 24 2022

Crossrefs

Cf. A082045, A082046, A082107.

Sequence in context: A358655 A258341 A054128 * A370306 A341803 A375273

Adjacent sequences: A082044 A082045 A082046 * A082048 A082049 A082050

Keyword

easy,nonn

Author

Paul Barry, Apr 03 2003

Status

approved