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Search: id:A100684
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| A100684 |
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Number of partitions of 2n free of multiples of 8 such that 4 occurs at most once. All odd parts occur with even multiplicities. There is no restriction on the other even parts. |
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+0
1
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| 1, 2, 4, 8, 12, 20, 32, 48, 72, 106, 152, 216, 305, 422, 580, 792, 1068, 1432, 1908, 2520, 3313, 4332, 5628, 7280, 9373, 12008, 15324, 19480, 24661, 31112, 39120, 49016, 61229, 76260, 94692, 117264, 144834, 178412, 219244, 268784, 328746
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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Noureddine Chair, Partition identities from partial supersymmetry.
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FORMULA
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G.f.: (1-x^4)*Product((1+x^(2*i))/(1-x^(2*i-1))^2, i=1..infinity). (Jovovic)
Expansion of (1-q^4)q^(-1/6)eta(q^4)eta(q^2)/eta(q)^2 in powers of q.
G.f.: (1-x^4) Prod_{k>0} (1+x^(2k))(1+x^k)^2. - Michael Somos Feb 10 2005
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (1-x^4)*eta(x^4+A)*eta(x^2+A)/eta(x+A)^2, n))} /* Michael Somos Feb 10 2005 */
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CROSSREFS
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Cf. A080054.
Sequence in context: A014557 A023598 A103258 this_sequence A131770 A163489 A076651
Adjacent sequences: A100681 A100682 A100683 this_sequence A100685 A100686 A100687
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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), Jan 27 2005
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EXTENSIONS
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Corrected by Vladeta Jovovic, Feb 01 2005
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