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%I #5 Oct 18 2020 07:09:14
%S 1,5,7,17,41,101,239,577,1393,3365,8119,19601,47321,114245,275807,
%T 665857,1607521,3880901,9369319,22619537,54608393,131836325,318281039,
%U 768398401,1855077841,4478554085,10812186007,26102926097,63018038201
%N Logarithmic derivative of the g.f. of A113281.
%F 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.
%F a(n) ~ (1 + sqrt(2))^(n+1) / 2. - _Vaclav Kotesovec_, Oct 18 2020
%o (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)}
%Y Cf. A113281, A113283, A113284.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Oct 22 2005
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