%I #31 Jul 19 2016 10:50:00

%S 1,2,3,6,7,12,16,26,31,42,59,72,104,116,184,186,303,282,497,406,783,

%T 612,1224,840,1856,1232,2784,1656,4136,2376,6008,3138,8735,4362,12345,

%U 5754,17693,7756,24432,10170,34471,13302,46771,17688,65144,22296,87008

%N Self-convolution of A073711.

%C The g.f. G(x) of A073711 satisfies: G(x) = G(x^2) + x*G(x^2)^2.

%C The terms of this sequence found at odd-indexed positions are equal to twice that of A194279, which equals the self-convolution cube of A073711.

%H Reinhard Zumkeller, <a href="/A073712/b073712.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A073711(2*n+1) for n>=0.

%F a(2*n+1) = 2*A194279(n) for n>=0, where A194279 equals the self-convolution cube of A073711.

%t nmax = 46; max = 2*nmax+1; f[x_] := Sum[ a[k]*x^k, {k, 0, max}]; a[0] = a[1] = a[2] = 1; coes = CoefficientList[ Series[ f[x] - f[x^2] - x*f[x^2]^2, {x, 0, max}], x]; sol = Solve[ Thread[ coes == 0]] // First; Table[ a[2*n+1], {n, 0, nmax}] /. sol (* _Jean-François Alcover_, Mar 06 2013 *)

%o (Haskell)

%o a073712 n = a073712_list !! n

%o a073712_list = map (g a073711_list) [1..] where

%o g xs k = sum $ zipWith (*) xs $ reverse $ take k xs

%o -- _Reinhard Zumkeller_, Dec 20 2012

%o (PARI) a(n)=local(A=1); for(i=0,#binary(n), A=subst(A,x,x^2+x*O(x^n))+x*subst(A,x,x^2+x*O(x^n))^2);polcoeff(A^2,n)

%o for(n=0,65,print1(a(n),", ")) \\ _Paul D. Hanna_, Dec 21 2012

%Y Cf. A073711, A194279.

%K easy,nice,nonn,look

%O 0,2

%A _Paul D. Hanna_, Aug 05 2002

%E Name changed and entry revised by _Paul D. Hanna_, Dec 21 2012