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

0,3

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).

Links

Table of n, a(n) for n=0..30.

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

Crossrefs

Cf. A113282, A113283, A113284.

Sequence in context: A077229 A335098 A018113 * A037446 A113151 A269964

Adjacent sequences: A113278 A113279 A113280 * A113282 A113283 A113284

Keyword

nonn

Author

Paul D. Hanna, Oct 22 2005

Status

approved