A113281 Self-convolution equals A113224.

1, 1, 3, 5, 11, 23, 51, 113, 255, 579, 1325, 3047, 7039, 16319, 37951, 88489, 206799, 484255, 1135969, 2668951, 6279509, 14793169, 34889553, 82372723, 194664283, 460436551, 1089943229, 2582033519, 6120967411, 14519686915, 34463104999

Offset: 0

Author

Paul D. Hanna, Oct 22 2005

Keywords

• nonn

Comments

Convolution of bisections A113283 and A113284 yields A082639, which is a bisection of the self-convolution of this sequence. Terms of the logarithmic derivative A113282 are related to the self-convolution A113224 by: A113282(2*n) = A113224(2*n), A113282(4*n+1) = 3 + A113224(4*n+1), A113282(4*n+3) = 1 + A113224(4*n+3).

Crossrefs

Cf. A113282, A113283, A113284.

Formula

G.f.: A(x) = ( (1+x^2)/(1-x^2)/(1-2*x-x^2) )^(1/2).

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