A113282 Logarithmic derivative of the g.f. of A113281.

1, 5, 7, 17, 41, 101, 239, 577, 1393, 3365, 8119, 19601, 47321, 114245, 275807, 665857, 1607521, 3880901, 9369319, 22619537, 54608393, 131836325, 318281039, 768398401, 1855077841, 4478554085, 10812186007, 26102926097, 63018038201

Offset: 0

Author

Paul D. Hanna, Oct 22 2005

Keywords

• nonn

Crossrefs

Cf. A113281, A113283, A113284.

Programs

PARI

{a(n)=local(x=X+X*O(X^n)); polcoeff((1+x^2)/(1-x^2)/(1-2*x-x^2) + x*(3+x^2)/(1-x^4),n,X)}

Formula

G.f.: (1+x^2)/(1-x^2)/(1-2*x-x^2) + x*(3+x^2)/(1-x^4). a(2*n) = A113224(2*n), a(4*n+1) = 3 + A113224(4*n+1), a(4*n+3) = 1 + A113224(4*n+3), where A113224 is the self-convolution of A113281.

a(n) ~ (1 + sqrt(2))^(n+1) / 2. - Vaclav Kotesovec, Oct 18 2020