A113281 - OEIS

%I #5 Oct 18 2020 07:07:29

%S 1,1,3,5,11,23,51,113,255,579,1325,3047,7039,16319,37951,88489,206799,

%T 484255,1135969,2668951,6279509,14793169,34889553,82372723,194664283,

%U 460436551,1089943229,2582033519,6120967411,14519686915,34463104999

%N Self-convolution equals A113224.

%C 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).

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

%F a(n) ~ (1 + sqrt(2))^(n + 1/2) / sqrt(2*Pi*n). - _Vaclav Kotesovec_, Oct 18 2020

%Y Cf. A113282, A113283, A113284.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 22 2005