Search: id:A121373
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%I A121373
%S A121373 1,1,1,0,0,1,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,
%T A121373 1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
%U A121373 1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0
%V A121373 1,1,-1,0,0,-1,0,-1,0,0,0,0,-1,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,
               0,0,1,0,0,0,0,
%W A121373 -1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,
               0,0,0,0,1,0,0,0,
%X A121373 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0
%N A121373 Expansion of f(q) = f(q, -q^2) in powers of q where f(q,r) is the Ramanujan 
               two variable theta function.
%F A121373 Euler transform of period 4 sequence [ 1, -2, 1, -1, ...].
%F A121373 a(n)=b(24n+1) where b(n) is multiplicative and b(p^2e)=(-1)^e if p = 
               7,11,13,17 (mod 24), b(p^2e)=+1 if p = 1,5,19,23 (mod 24) and b(p^(2e-1))=b(2^e)=b(3^e)=0 
               if e>0.
%F A121373 G.f.: (1+x)(1-x^2)(1+x^3)(1-x^4)...
%F A121373 G.f.: 1 +x -x^2(1+x) +x^3(1+x)(1-x^2) -x^4(1+x)(1-x^2)(1+x^3) +...
%F A121373 a(5n+3)=a(5n+4)=0. a(25n+1)=a(n).
%F A121373 G.f. Sum_{k>=0} a(k) x^(24k+1) = Sum_{k} (-1)^[(k+1)/2] x^(6k+1)^2.
%F A121373 Expansion of q^-1*eta(24z) in powers of -(q^24) where q=exp(2*pi*i*z).
%e A121373 eta(1/2+24z) = q +q^25 -q^49 -q^121 -q^169 -q^289 +q^361 +q^529 +...
%o A121373 (PARI) a(n)=if(issquare(24*n+1, &n), kronecker(24, n))
%o A121373 (PARI) a(n)=if(n<0, 0, polcoeff(eta(-x+x*O(x^n)), n))
%Y A121373 A010815(n)=(-1)^n*a(n). A080995(n)=|a(n)|.
%Y A121373 Sequence in context: A133080 A010815 A080995 this_sequence A133985 A143062 
               A074910
%Y A121373 Adjacent sequences: A121370 A121371 A121372 this_sequence A121374 A121375 
               A121376
%K A121373 sign
%O A121373 0,1
%A A121373 Michael Somos, Jul 24 2006

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