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Search: id:A097195
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| A097195 |
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G.f.: s(12)^3*s(18)^2/(s(6)^2*s(36)), where s(k) := subs(q=q^k, eta(q)) and eta(q) is Dedekind's function, cf. A010815. Then replace q^6 by q. |
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+0
12
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| 1, 2, 2, 2, 1, 2, 2, 2, 3, 0, 2, 2, 2, 2, 0, 4, 2, 2, 2, 0, 1, 2, 4, 2, 0, 2, 2, 2, 3, 2, 2, 0, 2, 2, 0, 2, 4, 2, 2, 0, 2, 4, 0, 4, 0, 2, 2, 2, 1, 0, 4, 2, 2, 0, 2, 2, 2, 4, 2, 0, 3, 2, 2, 2, 0, 0, 2, 4, 2, 0, 2, 4, 2, 2, 0, 0, 2, 2, 4, 2, 4, 2, 0, 2, 0, 4, 0, 2, 1, 0, 2, 2, 4, 4, 0, 2, 2, 0, 4, 0, 2, 2, 2, 2, 1
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 80, Eq. (32.38).
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FORMULA
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Fine gives an explicit formula for a(n) in terms of the divisors of n.
a(n)=b(6n+1) where b(n) is multiplicative and b(2^e) = b(3^e) = 0^e, b(p^e) = e+1 if p == 1 (mod 6), b(p^e) = (1+(-1)^e)/2 if p == 5 (mod 6)
G.f.: Sum_{k} x^k/(1-x^(6k+1)) . - Michael Somos Nov 03 2005
G.f.: Sum_{k>=0} a(k)x^(6k+1) = Sum_{k>0} x^(2k-1)*(1-x^(4k-2))*(1-x^(8k-4))*(1-x^(20k-10))/(1-x^(36k-18)) . - Michael Somos Nov 03 2005
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PROGRAM
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(PARI) a(n)=if(n<0, 0, sumdiv(6*n+1, d, kronecker(-3, d))) /* Michael Somos Nov 03 2005 */
(PARI) {a(n)=local(A, p, e); if(n<0, 0, n=6*n+1; A=factor(n); prod(k=1, matsize(A)[1], if(p=A[k, 1], e=A[k, 2]; if(p>3, if(p%6==1, e+1, !(e%2))))))} /* Michael Somos Nov 03 2005 */
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^3*eta(x^3+A)^2/ eta(x+A)^2/eta(x^6+A), n))} /* Michael Somos Nov 03 2005 */
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CROSSREFS
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Sequence in context: A122922 A046799 A037809 this_sequence A129451 A008334 A116858
Adjacent sequences: A097192 A097193 A097194 this_sequence A097196 A097197 A097198
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KEYWORD
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nonn,easy
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AUTHOR
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njas, Sep 16 2004
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