A103768 a(n) = (29*3^n - 18(n + 3)*2^n + 6n^2 + 24n + 27)/12.

0, 0, 6, 46, 228, 930, 3406, 11682, 38412, 122806, 385182, 1192254, 3656452, 11141178, 33791934, 102161962, 308156748, 928008846, 2791497262, 8390220006, 25203689700, 75680274610, 227185526766, 681858569586, 2046204853708

Offset: 0

Author

Henry Bottomley, Feb 15 2005

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-40,82,-91,52,-12).

Programs

Mathematica

Table[(29*3^n-18(n+3)2^n+6n^2+24n+27)/12,{n,40}] (* or *) LinearRecurrence[ {10,-40,82,-91,52,-12},{0,0,6,46,228,930},40] (* Harvey P. Dale, Aug 31 2018 *)

PARI

concat([0,0], Vec(-2*x^2*(x^3-4*x^2+7*x-3)/((x-1)^3*(2*x-1)^2*(3*x-1)) + O(x^100))) \\ Colin Barker, Sep 13 2014

Formula

a(n) = A078341(n, 3) = 3a(n-1)+n*A095151(n-1).

G.f.: -2*x^2*(x^3-4*x^2+7*x-3) / ((x-1)^3*(2*x-1)^2*(3*x-1)). - Colin Barker, Sep 13 2014