A133409 Zero followed by partial sums of A133405.

0, 0, 0, 0, 1, 4, 13, 39, 117, 351, 1054, 3163, 9490, 28470, 85410, 256230, 768691, 2306074, 6918223, 20754669, 62264007, 186792021, 560376064, 1681128193, 5043384580, 15130153740, 45390461220, 136171383660

Offset: 0

Author

Paul Curtz, Nov 25 2007

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-3,-1,4,-3).

Crossrefs

Cf. A088911, A133405.

Programs

Mathematica

Join[{0},Accumulate[LinearRecurrence[{3,0,-1,3},{0,0,0,1},40]]] (* or *) LinearRecurrence[{4,-3,-1,4,-3},{0,0,0,0,1},40] (* Harvey P. Dale, Dec 24 2013 *)

Formula

a(n+1)-3*a(n) = A088911(n+3).

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

O.g.f.: x^4/((3*x-1)*(1+x)*(x^2-x+1)*(x-1)). - R. J. Mathar, Jul 16 2008

Extensions

Edited and extended by R. J. Mathar, Jul 16 2008