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Search: id:A123863
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| A123863 |
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Expansion of (c(q^3)-c(q^6)-2*c(q^12))/3 in powers of q where c(q) is a cubic AGM analog function. |
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+0
1
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| 1, -1, 0, -1, 0, 0, 2, -1, 0, 0, 0, 0, 2, -2, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 1, -2, 0, -2, 0, 0, 2, -1, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, -1, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 2, -2, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 2, -2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, -3, 0, -1, 0, 0, 2, -2, 0
(list; graph; listen)
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OFFSET
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1,7
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FORMULA
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Expansion of eta(q)eta(q^4)eta(q^18)^4/(eta(q^2)eta(q^6)eta(q^36)) in powers of q.
Euler transform of period 36 sequence [ -1, 0, -1, -1, -1, 1, -1, -1, 0, 0, -1, 0, -1, 0, -1, -1, -1, -2, -1, -1, -1, 0, -1, 0, -1, 0, 0, -1, -1, 1, -1, -1, -1, 0, -1, -2, ...].
a(n) is multiplicative with a(2^e) = -1 if e>0, a(3^e) = 0^e, a(p^e) = e+1 if p == 1 (mod 6), a(p^e) = (1+(-1)^e)/2 if p == 5 (mod 6).
a(3n)=a(6n+5)=0.
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PROGRAM
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(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( eta(x+A)*eta(x^4+A)*eta(x^18+A)^4/ (eta(x^2+A)*eta(x^6+A)*eta(x^9+A)*eta(x^36+A)), n))}
(PARI) {a(n)=local(A, p, e); if(n<1, 0, A=factor(n); prod( k=1, matsize(A)[1], if(p=A[k, 1], e=A[k, 2]; if(p==2, -1, if(p==3, 0, if(p%6==1, e+1, !(e%2)))))))}
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CROSSREFS
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A113448(n)=-a(2n). A033687(n)=-a(6n+2).
Sequence in context: A112208 A048158 A113448 this_sequence A035195 A073797 A037856
Adjacent sequences: A123860 A123861 A123862 this_sequence A123864 A123865 A123866
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KEYWORD
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sign,mult
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AUTHOR
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Michael Somos, Oct 14 2006
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