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Search: id:A045833
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| A045833 |
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Expansion of eta(q^9)^3/eta(q^3) in powers of q. |
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+0
2
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| 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0
(list; graph; listen)
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OFFSET
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0,8
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FORMULA
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Euler transform of period 9 sequence [0, 0, 1, 0, 0, 1, 0, 0, -2, ...]. - Michael Somos, May 25 2005
G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w)=u^2*w-2u*w^2-v^3. - Michael Somos May 25 2005
G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^3), A(x^6)) where f(u1, u2, u3, u6)=u1*u3^2+u1*u6^2-u1*u3*u6-u2^2*u3. - Michael Somos May 25 2005
a(3n)=a(3n+2)=0. a(3n+1)=A033687(n). a(6n+1)=A097195(n). 3*a(n)=A033685(n).
Multiplicative with a(3^e) = 0 if e>0, a(p^e) = e+1 if p == 1 (mod 3), a(p^e) = (1+(-1)^e)/2 if p == 2 (mod 3). - Michael Somos May 25 2005
G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^3), A(x^6)) where f(u1, u2, u3, u6)=u2*u3^2+2*u2*u3*u6+4*u2*u6^2-u1^2*u6. - Michael Somos May 25 2005
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EXAMPLE
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q +q^4 +2*q^7 +2*q^13 +q^16 +2*q^19 +q^25 +2*q^28 +2*q^31 +...
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PROGRAM
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(PARI) {a(n)=local(A, p, e); if(n<0, 0, A=factor(n); prod(k=1, matsize(A)[1], if(p=A[k, 1], e=A[k, 2]; if(p!=3, if(p%3==1, e+1, !(e%2))))))} /* Michael Somos May 25 2005 */
(PARI) {a(n)=local(A); if((n<1)|(n%3!=1), 0, n=(n-1)/3; A=x*O(x^n); polcoeff( eta(x^3+A)^3/eta(x+A), n))} /* Michael Somos May 25 2005 */
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CROSSREFS
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Sequence in context: A045838 A045837 A126825 this_sequence A117896 A132976 A028649
Adjacent sequences: A045830 A045831 A045832 this_sequence A045834 A045835 A045836
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KEYWORD
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nonn,mult
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AUTHOR
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njas
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