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Search: id:A098151
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| A098151 |
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Number of partitions of 2n prime to 3 with all odd parts occurring with even multiplicities. There is no restriction on the even parts. |
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8
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| 1, 2, 4, 6, 10, 16, 24, 36, 52, 74, 104, 144, 198, 268, 360, 480, 634, 832, 1084, 1404, 1808, 2316, 2952, 3744, 4728, 5946, 7448, 9294, 11556, 14320, 17688, 21780, 26740, 32736, 39968, 48672, 59122, 71644, 86616, 104484, 125768, 151072, 181104, 216684
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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G.f. A(x) satisfies 0=f(A(x),A(x^3)) where f(u,v)=u^3-v+3uv^2-3u^2v^3. Michael Somos Dec 04 2004
Expansion of eta(q^2)eta(q^3)^2/(eta(q)^2eta(q^6)) in powers of q.
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REFERENCES
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Noureddine Chair, Partition Identities From Partial Supersymmetry, to be submitted
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FORMULA
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Euler transform of period 6 sequence [2, 1, 0, 1, 2, 0, ...]. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 24 2004
Taylor series of product_{k=1..inf}(1+x^k+x^(2*k))/(1-x^k+x^(2*k))= product_{k=1..inf}(1+x^k)(1-x^(3k))/((1-x^k)(1+x^(3k)))=Theta_4(0, x^3)/theta_4(0, x)
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EXAMPLE
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E.g a(4)=10 because 8=4+4=4+2+2=2+2+2+2=2+2+2+1+1=2+2+1+1+1+1=4+2+1+1=4+1+1+1+1=2+1+1+1+1=1+1+1+1+1+1+1+1=...
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MAPLE
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series(product((1+x^k+x^(2*k))/(1-x^k+x^(2*k)), k=1..150), x=0, 100);
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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)*eta(x^3+A)^2/eta(x+A)^2/eta(x^6+A), n)) /* Michael Somos Dec 04 2004 */
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CROSSREFS
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Cf. A015128.
Sequence in context: A073150 A132212 A137414 this_sequence A132002 A028445 A006305
Adjacent sequences: A098148 A098149 A098150 this_sequence A098152 A098153 A098154
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KEYWORD
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nonn
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AUTHOR
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Noureddine Chair (n.chair(AT)rocketmail.com), Aug 29 2004
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