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

0,1

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).

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

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

Crossrefs

Sequence in context: A255600 A320809 A287967 * A149862 A149863 A371714

Adjacent sequences: A133445 A133446 A133447 * A133449 A133450 A133451

Keyword

nonn,easy

Author

Paul Curtz, Nov 27 2007

Status

approved