A082107 Diagonal sums of number array A082105.

1, 2, 8, 28, 79, 190, 406, 792, 1437, 2458, 4004, 6260, 9451, 13846, 19762, 27568, 37689, 50610, 66880, 87116, 112007, 142318, 178894, 222664, 274645, 335946, 407772, 491428, 588323, 699974, 828010, 974176, 1140337, 1328482, 1540728

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 + 20*n^3 + 9*n + 30)/30.

G.f.: (1-4*x+11*x^2-10*x^3+6*x^4)/(1-x)^6 . - R. J. Mathar, Mar 27 2019

E.g.f.: (1/30)*(30 +30*x +75*x^2 +45*x^3 +10*x^4 +x^5)*exp(x). - G. C. Greubel, Dec 22 2022

Mathematica

LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 2, 8, 28, 79, 190}, 51] (* G. C. Greubel, Dec 22 2022 *)

Prog

(Magma) [(n^5+20*n^3+9*n+30)/30: n in [0..50]]; // G. C. Greubel, Dec 22 2022
(SageMath) [(n^5+20*n^3+9*n+30)/30 for n in range(51)] # G. C. Greubel, Dec 22 2022

Crossrefs

Cf. A082043, A082045, A082046, A082105, A082106, A082109, A082110.

Sequence in context: A170871 A245996 A229935 * A135263 A048497 A118047

Adjacent sequences: A082104 A082105 A082106 * A082108 A082109 A082110

Keyword

easy,nonn

Author

Paul Barry, Apr 03 2003

Status

approved