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

0,2

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+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

Mathematica

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

Prog

(Magma) [(n^5+10*n^3+19*n+30)/30: n in [0..40]]; // G. C. Greubel, Dec 24 2022
(SageMath) [(n^5+10*n^3+19*n+30)/30 for n in range(41)] # G. C. Greubel, Dec 24 2022

Crossrefs

Cf. A082043, A082047.

Sequence in context: A110295 A027294 A231538 * A358301 A361732 A005628

Adjacent sequences: A082042 A082043 A082044 * A082046 A082047 A082048

Keyword

easy,nonn

Author

Paul Barry, Apr 03 2003

Status

approved