%I #10 Jun 13 2015 00:51:22

%S 0,1,1,6,15,45,120,325,861,2278,5995,15753,41328,108345,283881,743590,

%T 1947351,5099221,13351528,34957341,91523685,239618886,627341331,

%U 1642418641,4299936480,11257426225,29472399505,77159865030,202007345631

%N Fib(n)(2Fib(n)-1).

%C mod(A095122(n),2)=mod(Fib(n),2)=A011655(n)

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-5,-1,1).

%F G.f. : x(1-2x+2x^2+x^3)/((1+x)(1-x-x^2)(1-3x+x^2));

%F a(n)=2(Fib(2n-1)+Fib(2n+1))/5-Fib(n)+4(-1)^n/5;

%F a(n)=2L(2n)/5-Fib(n)+4(-1)^n/5;

%F a(n)=2*A000032(2n)/5-A000045(n)+4(-1)^n/5.

%F a(0)=0, a(1)=1, a(2)=1, a(3)=6, a(4)=15, a(n)=3*a(n-1)+a(n-2)- 5*a(n-3)- a(n-4)+a(n-5) [From Harvey P. Dale, Jan 14 2012]

%t #(2#-1)&/@Fibonacci[Range[0,30]] (* or *) LinearRecurrence[{3,1,-5,-1,1},{0,1,1,6,15},30] (* _Harvey P. Dale_, Jan 14 2012 *)

%K easy,nonn

%O 0,4

%A _Paul Barry_, May 29 2004