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Search: id:A100928
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| A100928 |
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Number of partitions of n into parts free of odd octagonal (star) numbers: k(3k-2) and the only number with multiplicity in the unrestricted partitions is the number 2 with multiplicity of the form :4k+2l, k a positive integer and l=0,1. |
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1
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| 1, 0, 1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 9, 12, 14, 18, 21, 26, 31, 37, 44, 52, 62, 73, 86, 101, 118, 138, 160, 186, 216, 249, 288, 332, 381, 438, 501, 573, 655, 746, 851, 966, 1099, 1244, 1410, 1595, 1801, 2033, 2292, 2580, 2903, 3261, 3660, 4105, 4598, 5147, 5755
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OFFSET
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1,6
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COMMENT
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Thia is also the inverted graded of the generating function for partitions of n into parts free of octagonal numbers.
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REFERENCES
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Noureddine Chair, Partition Identities From Partial Supersymmetry, hep-th/040911 2004.
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-(-1)^kx^(3k^2-2k)).
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EXAMPLE
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E.g. a(15)=18 because 15=13+5=12+3=11+4=10+5=10+3+2=9+6=9+4+2=8+7=8+4+3=8+5+2=7+6+2=7+5+3=6+5+4=6+4+3+2=5+2+2+2+2+2=7+2+2+2+2=4+3+2+2+2+2.
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MAPLE
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series(product((1+x^k)/(1-(-1)^k*x^(3*k^(2)-2*k)), k=1..100), x=0, 100);
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CROSSREFS
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Sequence in context: A008582 A069911 A027196 this_sequence A034140 A109950 A008674
Adjacent sequences: A100925 A100926 A100927 this_sequence A100929 A100930 A100931
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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 23 2004
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