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Search: id:A122071
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| A122071 |
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Sum over divisors d of 2n+1 of kronecker(-18/d). |
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+0
1
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| 1, 1, 0, 0, 1, 2, 0, 0, 2, 2, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 1, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 3, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 1, 2, 0, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 4
(list; graph; listen)
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OFFSET
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0,6
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REFERENCES
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N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 83, Eq. (32.58).
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FORMULA
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Expansion of q^(-1/2)eta(q^2)^2eta(q^3)eta(q^8)eta(q^12)^3/(eta(q)eta(q^4)^2eta(q^6)eta(q^24)) in powers of q.
Euler transform of period 24 sequence [ 1, -1, 0, 1, 1, -1, 1, 0, 0, -1, 1, -2, 1, -1, 0, 0, 1, -1, 1, 1, 0, -1, 1, -2, ...].
a(n)=b(2n+1) where b(n) is multiplicative and b(2^e)=0^e, b(3^e)=1, b(p^e) = e+1 if p == 1,3 (mod 8), b(p^e) = (1+(-1)^e)/2 if p == 5,7 (mod 8).
G.f.: Sum_{k>0} x^k(1-x^(4k-2))(1-x^(6k-3))/(1+x^(12k-6)).
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PROGRAM
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(PARI) {a(n)=if(n<0, 0, n=2*n+1; sumdiv(n, d, kronecker(-18, d)))}
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^2*eta(x^3+A)*eta(x^8+A)*eta(x^12+A)^3/ eta(x+A)/eta(x^4+A)^2/eta(x^6+A)/eta(x^24+A), n))}
(PARI) {a(n)=local(A, p, e); if(n<0, 0, n=2*n+1; A=factor(n); prod(k=1, matsize(A)[1], if(p=A[k, 1], e=A[k, 2]; if(p==2, 0, if(p==3, 1, if(p%8<4, e+1, (1+(-1)^e)/2))))))}
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CROSSREFS
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A035172(2n+1)=a(n).
Sequence in context: A130454 A070787 A033985 this_sequence A099766 A132339 A137676
Adjacent sequences: A122068 A122069 A122070 this_sequence A122072 A122073 A122074
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Aug 20 2006
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