A290061 a(n) = (1/24)*(n + 3)*(3*n^3 + 5*n^2 - 6*n + 16).

3, 10, 31, 77, 162, 303, 520, 836, 1277, 1872, 2653, 3655, 4916, 6477, 8382, 10678, 13415, 16646, 20427, 24817, 29878, 35675, 42276, 49752, 58177, 67628, 78185, 89931, 102952, 117337, 133178, 150570, 169611, 190402, 213047, 237653, 264330, 293191, 324352, 357932

Offset: 1

Author

Gregory Gerard Wojnar, Jul 19 2017

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Column 3 of A290053.

Programs

Mathematica

Table[(1/24)(n+3)(3n^3+5n^2-6n+16),{n,40}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{3,10,31,77,162},40] (* Harvey P. Dale, Oct 29 2018 *)

PARI

Vec(x*(3 - 5*x + 11*x^2 - 8*x^3 + 2*x^4) / (1 - x)^5 + O(x^50)) \\ Colin Barker, Jul 20 2017

PARI

vector(50,n,(n+3)*(3*n^3+5*n^2-6*n+16)/24) \\ Derek Orr, Jul 24 2017

Formula

From Colin Barker, Jul 20 2017: (Start)

G.f.: x*(3 - 5*x + 11*x^2 - 8*x^3 + 2*x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 4.

(End)