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A101230
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Number of partitions of 2n in which both odd parts and parts that are multiples of 3 occur with even multiplicities. There is no restriction on the other even parts.
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1, 2, 4, 7, 12, 20, 32, 50, 76, 113, 166, 240, 343, 484, 676, 935, 1282, 1744, 2355, 3158, 4208, 5573, 7340, 9616, 12536, 16266, 21012, 27028, 34628, 44196, 56204, 71226, 89964, 113270, 142180, 177948, 222089, 276430, 343172, 424959, 524966
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| Noureddine Chair, Partition Identities From Partial Supersymmetry, hep-th/0409011 Sep 01 2004.
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FORMULA
| G.f.:=product_{k>0}(1+x^k)/((1-x^k)(1+x^(3k)))= Theta_4(0, x^3)/theta(0, x)1/product_{k>0}(1-x^(3k)).
Euler transform of period 6 sequence [2, 1, 1, 1, 2, 1, ...]. - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 17 2004
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EXAMPLE
| a(8)=12 because 8=4+4=4+2+2=4+2+1+1=4+1+1+1+1=3+3+2=3+3+1+1=2+2+2+2=2+2+2+1+1=2+2+1+1+1+1=2+1+1+1+1+1+1=1+1+1+1+1+1+1+1
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MAPLE
| series(product((1+x^k)/((1-x^k)*(1+x^(3*k))), k=1..100), x=0, 100);
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CROSSREFS
| Cf. A015128, A098151.
Sequence in context: A193840 A036372 A132218 * A128129 A014968 A126348
Adjacent sequences: A101227 A101228 A101229 * A101231 A101232 A101233
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KEYWORD
| nonn
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AUTHOR
| Noureddine Chair (n.chair(AT)rocketmail.com), Dec 16 2004
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