Search: id:A113681
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%I A113681
%S A113681 1,1,0,1,0,0,0,1,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0,
%T A113681 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,
%U A113681 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0
%V A113681 1,1,0,-1,0,0,0,-1,-1,0,0,0,0,0,-1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,1,0,
               0,0,0,0,0,0,0,0,
%W A113681 0,1,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,-1,0,0,0,0,
               0,0,0,0,0,0,0,0,
%X A113681 0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0
%N A113681 Expansion of f(-x^2,-x^3)^2/f(-x,-x^2) in powers of x.
%C A113681 f(a,b)=Sum_{k} a^((k^2+k)/2)*b^((k^2-k)/2) is Ramanujan's two-variable 
               theta function.
%F A113681 Euler transform of period 5 sequence [1, -1, -1, 1, -1, ...].
%F A113681 G.f.: Sum_{k} (-1)^k(x^((15k^2-k)/2) +x^((15k^2-11k)/2+1)).
%F A113681 G.f.: Product_{k>0} (1-x^(5k))(1-x^(5k-2))(1-x^(5k-3))/((1-x^(5k-1))(1-x^(5k-4))).
%o A113681 (PARI) {a(n)=if(n<0, 0, polcoeff( prod(k=1,n,(1-x^k)^((k%5==0)-kronecker(5,
               k)),1+x*O(x^n)), n))}
%o A113681 (PARI) {a(n)=n*=5; if(issquare(24*n+1, &n), kronecker(12, n))}
%Y A113681 Cf. A113430. A010815(5n)=a(n).
%Y A113681 Sequence in context: A036987 A143259 A113430 this_sequence A155972 A010054 
               A106459
%Y A113681 Adjacent sequences: A113678 A113679 A113680 this_sequence A113682 A113683 
               A113684
%K A113681 sign
%O A113681 0,1
%A A113681 Michael Somos, Nov 04 2005

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