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A103257
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Number of partitions of 2n free of multiples of 5. All odd parts occur with multiplicity 2 or 4. the even parts occur at most twice.
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1
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1, 2, 4, 6, 10, 14, 20, 28, 40, 54, 72, 96, 126, 164, 212, 272, 346, 436, 548, 684, 850, 1052, 1296, 1588, 1940, 2362, 2864, 3462, 4172, 5012, 6004, 7172, 8548, 10160, 12048, 14256, 16830, 19828, 23312, 27356, 32040
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| N. Chair, Partition identities from partial supersymmetry.
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FORMULA
| G.f.: (theta_4(0, x^3)*theta_4(0, x^5))/theta_4(0, x).
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EXAMPLE
| E.g. a(10) = 14 because 10 can be written as 8+2 = 8+1+1 = 6+4 = 6+2+2 = 6+2+1+1 = 6+1+1+1+1 = 4+4+2 = 4+4+1+1 = 4+3+3 = 4+2+2+1+1 = 4+2+1+1+1+1 = 3+3+2+2 = 3+3+2+1+1 = 3+3+1+1+1+1.
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MAPLE
| series(product(((1+x^k)*(1-x^(3*k))*(1-x^(5*k)))/((1-x^k)*(1+x^(3*k))*(1-x^(5*k))), k=1..100), x=0, 100);
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CROSSREFS
| Cf. A098151.
Sequence in context: A088932 A088954 A000123 * A103259 A082380 A136460
Adjacent sequences: A103254 A103255 A103256 * A103258 A103259 A103260
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KEYWORD
| nonn
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AUTHOR
| Noureddine Chair (n.chair(AT)rocketmail.com), Jan 27 2005
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