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

1,1

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).

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)

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 *)

Prog

(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

Crossrefs

Column 3 of A290053.

Sequence in context: A316764 A331780 A360563 * A212031 A339032 A374925

Adjacent sequences: A290058 A290059 A290060 * A290062 A290063 A290064

Keyword

nonn,easy

Author

Gregory Gerard Wojnar, Jul 19 2017

Status

approved