A082045 Diagonal sums of number array A082043.

1, 2, 6, 20, 59, 150, 336, 680, 1269, 2218, 3674, 5820, 8879, 13118, 18852, 26448, 36329, 48978, 64942, 84836, 109347, 139238, 175352, 218616, 270045, 330746, 401922, 484876, 581015, 691854, 819020, 964256, 1129425, 1316514, 1527638

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. A082043, A082047.

Programs

Magma

[(n^5+10*n^3+19*n+30)/30: n in [0..40]]; // G. C. Greubel, Dec 24 2022

Mathematica

LinearRecurrence[{6,-15,20,-15,6,-1},{1,2,6,20,59,150},41] (* Harvey P. Dale, Mar 18 2018 *)

SageMath

[(n^5+10*n^3+19*n+30)/30 for n in range(41)] # G. C. Greubel, Dec 24 2022

Formula

a(n) = (n^5+10*n^3+19*n+30)/30.

G.f.: (1-4*x+9*x^2-6*x^3+4*x^4)/(1-x)^6. - R. J. Mathar, Oct 29 2014

E.g.f.: (1/30)*(30 +30*x +45*x^2 +35*x^3 +10*x^4 +x^5)*exp(x). - G. C. Greubel, Dec 24 2022