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Search: id:A103257
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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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+0
2
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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; listen)
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OFFSET
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0,2
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REFERENCES
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N. Chair, Partition identities from partial supersymmetry.
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FORMULA
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G.f.: (theta_4(0, x^3)*theta_4(0, x^5))/theta_4(0, x).
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EXAMPLE
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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
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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
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Cf. A098151.
Sequence in context: A088932 A088954 A000123 this_sequence A103259 A082380 A136460
Adjacent sequences: A103254 A103255 A103256 this_sequence A103258 A103259 A103260
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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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