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Search: id:A121373
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| A121373 |
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Expansion of f(q) = f(q, -q^2) in powers of q where f(q,r) is the Ramanujan two variable theta function. |
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+0
1
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| 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, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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0,1
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FORMULA
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Euler transform of period 4 sequence [ 1, -2, 1, -1, ...].
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.
G.f.: (1+x)(1-x^2)(1+x^3)(1-x^4)...
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) +...
a(5n+3)=a(5n+4)=0. a(25n+1)=a(n).
G.f. Sum_{k>=0} a(k) x^(24k+1) = Sum_{k} (-1)^[(k+1)/2] x^(6k+1)^2.
Expansion of q^-1*eta(24z) in powers of -(q^24) where q=exp(2*pi*i*z).
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EXAMPLE
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eta(1/2+24z) = q +q^25 -q^49 -q^121 -q^169 -q^289 +q^361 +q^529 +...
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PROGRAM
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(PARI) a(n)=if(issquare(24*n+1, &n), kronecker(24, n))
(PARI) a(n)=if(n<0, 0, polcoeff(eta(-x+x*O(x^n)), n))
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CROSSREFS
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A010815(n)=(-1)^n*a(n). A080995(n)=|a(n)|.
Sequence in context: A133080 A010815 A080995 this_sequence A133985 A143062 A074910
Adjacent sequences: A121370 A121371 A121372 this_sequence A121374 A121375 A121376
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Jul 24 2006
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