A290061 - OEIS

%I #18 Oct 29 2018 17:46:28

%S 3,10,31,77,162,303,520,836,1277,1872,2653,3655,4916,6477,8382,10678,

%T 13415,16646,20427,24817,29878,35675,42276,49752,58177,67628,78185,

%U 89931,102952,117337,133178,150570,169611,190402,213047,237653,264330,293191,324352,357932

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

%H Colin Barker, <a href="/A290061/b290061.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F From _Colin Barker_, Jul 20 2017: (Start)

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

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

%F (End)

%t 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 *)

%o (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

%o (PARI) vector(50,n,(n+3)*(3*n^3+5*n^2-6*n+16)/24) \\ _Derek Orr_, Jul 24 2017

%Y Column 3 of A290053.

%K nonn,easy

%O 1,1

%A _Gregory Gerard Wojnar_, Jul 19 2017