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Search: id:A100927
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| A100927 |
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Number of partitions of n into distinct parts free of hexagonal numbers. |
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+0
2
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| 1, 0, 1, 1, 1, 2, 1, 3, 2, 4, 4, 5, 7, 7, 10, 10, 13, 15, 17, 21, 23, 29, 32, 38, 44, 50, 59, 66, 76, 87, 100, 113, 129, 147, 167, 189, 214, 241, 273, 307, 345, 388, 436, 489, 548, 612, 686, 765, 854, 951, 1059, 1180, 1309, 1456, 1614, 1791, 1985, 2196
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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This is also the inverted graded of the generating function of partitions into parts free of hexagonal numbers
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REFERENCES
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Noureddine Chair, Partititon Identities From Partial Supersymmetry, hep-th/0409011.
J. A. Sellers, Journal of Integer Sequences. 7(2004) Article 04.2.4.
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FORMULA
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G.f.:=product_{k>0}(1+x^k)/(1+x^(2k^2-k))= 1/product_{k>0}(1-x^k+x^(2k)-x^(3k)+...-x^(2k^2-3k)+x^(2k^2-2k))
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EXAMPLE
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E.g"a(16)=13 because 16=14+2=13+3=12+4=11+5=11+3+2=10+4+2=9+7=9+5+2=9+4+3=8+5+3=7+5+4=7+4+3+2"
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MAPLE
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series(product((1+x^k)/(1+x^(2*k^(2)-k)), k=1..100), x=0, 100);
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CROSSREFS
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Sequence in context: A034390 A144693 A029139 this_sequence A001687 A159072 A116928
Adjacent sequences: A100924 A100925 A100926 this_sequence A100928 A100929 A100930
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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 22 2004
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