A133448 a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4), with initial values 2,5,13,40.

2, 5, 13, 40, 121, 365, 1094, 3281, 9841, 29524, 88573, 265721, 797162, 2391485, 7174453, 21523360, 64570081, 193710245, 581130734, 1743392201, 5230176601, 15690529804, 47071589413, 141214768241, 423644304722, 1270932914165, 3812798742493, 11438396227480

Offset: 0

Author

Paul Curtz, Nov 27 2007

Keywords

• nonn
• easy

Links

• Robert Israel, Table of n, a(n) for n = 0..2093
• Index entries for linear recurrences with constant coefficients, signature (3,0,-1,3).

Programs

Maple

f:= gfun:-rectoproc({a(n)=3*a(n-1)-a(n-3)+3*a(n-4),a(0)=2,a(1)=5,a(2)=13,a(3)=40,a(4)=121},a(n),remember):
map(f, [$0..40]); # Robert Israel, Jun 08 2017

Formula

G.f.: ( -2+x+2*x^2-3*x^3 ) / ( (3*x-1)*(1+x)*(x^2-x+1) ). - Robert Israel, Jun 08 2017

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