A133453 a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4), with initial values 2,4,13,40.

2, 4, 13, 40, 122, 365, 1094, 3280, 9841, 29524, 88574, 265721, 797162, 2391484, 7174453, 21523360, 64570082, 193710245, 581130734, 1743392200, 5230176601, 15690529804, 47071589414, 141214768241, 423644304722, 1270932914164

Offset: 0

Author

Paul Curtz, Nov 27 2007

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (3,0,-1,3).

Crossrefs

Cf. A129339.

Programs

Mathematica

LinearRecurrence[{3,0,-1,3},{2,4,13,40},30] (* Harvey P. Dale, Sep 10 2018 *)

Formula

O.g.f: -(2 - 2*x + x^2 + 3*x^3)/((3*x-1)*(x+1)*(x^2-x+1)). - R. J. Mathar, Nov 30 2007

6*a(n) = 3^(n+2) +(-1)^n +2*A057079(n+2). - R. J. Mathar, Oct 03 2021