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Search: id:A100989
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| A100989 |
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Number of partitions of n into parts free of odd hexagonal numbers, and the only number with multiplicity in the unrestricted partitions is the number 2 with multiplicity of the form 3k+l, where k is a positive integer and l=0,1. |
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+0
1
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| 1, 0, 1, 1, 1, 2, 3, 3, 4, 6, 6, 9, 11, 13, 16, 20, 20, 23, 29, 35, 41, 49, 59, 68, 82, 96, 112, 131, 154, 178, 207, 242, 277, 321, 371, 425, 489, 562, 641, 733, 839, 953, 1086, 1236, 1399, 1588, 1798, 2032, 2295, 2592, 2917, 3285
(list; graph; listen)
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OFFSET
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1,6
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REFERENCES
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Noureddine Chair, Partition Identities From Partial Supersymmetry, hep-th/0409011.
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FORMULA
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G.f.:=product_{k>0}(1+x^k)/(1-(-1)^kx^(2k^2-k)).
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EXAMPLE
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E.g "a(15)=20 because
15=13+2=12+3=11+4=10+5=10+3+2=9+6=9+4+2=8+7=8+5+2=8+4+3=7+6+2=7+5+3=6+5+4=6+4+3+2=9+2+2+2=7+2+2+2+2=6+3+2+2+2=5+4+2+2+2=4+3+2+2+2+2=3+2+2+2+2+2+2"
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MAPLE
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series(product((1+x^k)/(1-(-1)^k*x^(2*k^2-k)), k=1..100), x=0, 100);
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CROSSREFS
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Cf. A100926, A100927.
Sequence in context: A106464 A093003 A118096 this_sequence A023158 A120882 A102187
Adjacent sequences: A100986 A100987 A100988 this_sequence A100990 A100991 A100992
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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), Nov 29 2004
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