A213787 a(n) = Sum_{1<=i

0, 0, 0, 2, 17, 102, 518, 2442, 11010, 48444, 209979, 902132, 3854708, 16416204, 69769244, 296148174, 1256077725, 5324954250, 22567665834, 95626443110, 405154147310, 1716454353240, 7271524823255, 30804002164872, 130491325800072, 552779233930872, 2341634254967448, 9919384305913082, 42019349641680905

Offset: 0

Author

N. J. A. Sloane, Jun 20 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (6, -2, -29, 16, 40, -11, -14, 2, 1).

Crossrefs

Cf. A000045, A190173.

Programs

Maple

a:= n-> (Matrix(9, (i, j)-> `if`(i=j-1, 1, `if`(i=9,
         [1, 2, -14, -11, 40, 16, -29, -2, 6][j], 0)))^(n+3).
         <<0, -1, 0, 0, 0, 0, 2, 17, 102>>)[1, 1]:
seq (a(n), n=0..30);  # Alois P. Heinz, Jun 20 2012

Mathematica

LinearRecurrence[{6, -2, -29, 16, 40, -11, -14, 2, 1}, {0, 0, 0, 2, 17, 102, 518, 2442, 11010}, 30] (* Jean-François Alcover, Feb 13 2016 *)

PARI

x='x+O('x^50); concat([0,0,0], Vec((x^4+2*x^3-4*x^2-5*x-2)*x^3 / ((x+1) * (x^2-x-1) * (x^2+4*x-1) * (x^2-3*x+1) * (x^2+x-1)))) \\ G. C. Greubel, Mar 05 2017

Formula

G.f.: (x^4+2*x^3-4*x^2-5*x-2)*x^3 / ((x+1) * (x^2-x-1) * (x^2+4*x-1) * (x^2-3*x+1) * (x^2+x-1)). - Alois P. Heinz, Jun 20 2012