A133448 - OEIS

%I #22 Feb 03 2025 18:53:38

%S 2,5,13,40,121,365,1094,3281,9841,29524,88573,265721,797162,2391485,

%T 7174453,21523360,64570081,193710245,581130734,1743392201,5230176601,

%U 15690529804,47071589413,141214768241,423644304722,1270932914165,3812798742493,11438396227480

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

%H Robert Israel, <a href="/A133448/b133448.txt">Table of n, a(n) for n = 0..2093</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-1,3).

%F G.f.: ( -2+x+2*x^2-3*x^3 ) / ( (3*x-1)*(1+x)*(x^2-x+1) ). - _Robert Israel_, Jun 08 2017

%F 6*a(n) = -(-1)^n +3^(n+2) +2*A057079(n+1). - _R. J. Mathar_, Oct 03 2021

%p 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):

%p map(f, [$0..40]); # _Robert Israel_, Jun 08 2017

%K nonn,easy

%O 0,1

%A _Paul Curtz_, Nov 27 2007