A133448 a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4).

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