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Search: id:A103259
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| A103259 |
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Number of partitions of 2n prime to 3,5 with all odd parts occurring with even multiplicities. There is no restriction on the even parts. |
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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, 274, 350, 444, 560, 704, 878, 1092, 1352, 1668, 2048, 2506, 3056, 3714, 4500, 5436, 6552, 7872, 9436, 11280, 13456, 16012, 19014, 22532, 26648, 31452
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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This is also the sequence A103257/(theta_4(0,x^(15)))
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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.: (theta_4(0, x^3)*theta_4(0, x^5))/(theta_4(0, x)*theta_4(0, x^(15))).
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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=4+4+2=4+4+1+1=4+2+2+2=
4+2+2+1+1 = 4+2+1+1+1+1 = 4+1+1+1+1+1+1 = 2+2+2+2+2 = 2+2+2+2+1+1 = 2+2+2+1+1+1+1 = 2+2+1+1+1+1+1+1 = 2+1+1+1+1+1+1+1+1 = 1+1+1+1+1+1+1+1+1+1.
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MAPLE
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seies(product((1+x^k)*(1-x^(3*k))*(1-x^(5*k))*(1+x^(15*k)))/(1-x^k)*(1+x^(3*k))*\ (1+x^(5*k))*(1-x^(15*k))), k=1..100), x=0, 100);
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CROSSREFS
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Cf. A102346, A103257.
Sequence in context: A088954 A000123 A103257 this_sequence A082380 A136460 A000065
Adjacent sequences: A103256 A103257 A103258 this_sequence A103260 A103261 A103262
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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), Feb 15 2005
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