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Search: id:A122865
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| A122865 |
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Expansion of chi(q)* phi(q^3)* psi(-q^3) in powers of q where chi(), phi(), psi() are Ramanujan theta functions. |
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+0
8
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| 1, 1, 0, 2, 2, 1, 0, 0, 3, 0, 0, 2, 2, 2, 0, 0, 1, 2, 0, 2, 2, 1, 0, 0, 2, 0, 0, 2, 4, 0, 0, 0, 2, 3, 0, 2, 2, 0, 0, 0, 1, 0, 0, 4, 0, 2, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 3, 0, 0, 2, 2, 0, 0, 0, 2, 1, 0, 2, 4, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 4, 0, 1, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 3, 2, 0, 2, 0, 0, 0, 0, 2
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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Expansion of q^(-1/3)*eta(q^2)^2*eta(q^6)^4/(eta(q)*eta(q^3)*eta(q^4)*eta(q^12)) in powers of q.
Euler transform of period 12 sequence [ 1, -1, 2, 0, 1, -4, 1, 0, 2, -1, 1, -2, ...]. - Michael Somos Apr 19 2007
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^2*eta(x^6+A)^4/ (eta(x+A)*eta(x^3+A)*eta(x^4+A)*eta(x^12+A)), n))}
(PARI) {a(n)=local(A, p, e); if(n<0, 0, n=3*n+1; 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, -2*(-1)^e, if(p%4==1, e+1, 1-e%2))))))}
(PARI) {a(n)=if(n<0, 0, n=3*n+1; sumdiv(n, d, (d%4==1) -(d%4==3)))} /* Michael Somos Apr 19 2007 */
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CROSSREFS
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A002654(3n+1)=A035154(3n+1)=A113446(3n+1)=A122864(3n+1)=a(n).
Sequence in context: A029390 A108040 A137566 this_sequence A074080 A111407 A084440
Adjacent sequences: A122862 A122863 A122864 this_sequence A122866 A122867 A122868
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Sep 15 2006
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