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

0,2

Links

Table of n, a(n) for n=0..28.

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

Prog

(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)}

Crossrefs

Cf. A113281, A113283, A113284.

Sequence in context: A318568 A239414 A163570 * A323200 A096741 A355188

Adjacent sequences: A113279 A113280 A113281 * A113283 A113284 A113285

Keyword

nonn

Author

Paul D. Hanna, Oct 22 2005

Status

approved