A097131 F(n)+(-1)^n*F(n-1).

1, 1, 2, 1, 5, 2, 13, 5, 34, 13, 89, 34, 233, 89, 610, 233, 1597, 610, 4181, 1597, 10946, 4181, 28657, 10946, 75025, 28657, 196418, 75025, 514229, 196418, 1346269, 514229, 3524578, 1346269, 9227465, 3524578, 24157817, 9227465, 63245986, 24157817

Offset: 0

Author

Paul Barry, Jul 26 2004

Keywords

• easy
• nonn

Crossrefs

Cf. A000045.

Formula

G.f. : x/(1-x-x^2)+(1+x)/(1+x-x^2)=(1+x-x^2-2x^3)/(1-3x^2+x^4); a(n)=3a(n-2)-a(n-4); a(2n)=F(2n+1); a(2n+1)=F(2n-1).

a(n)=A087123(n-1), n>0. [From R. J. Mathar, Sep 02 2008]