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Search: id:A100926
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| A100926 |
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Number of partitions of n into parts free of odd squares and the only number with multiplicity in the unrestricted partitions is the number 2. |
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+0
3
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| 1, 0, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 23, 27, 33, 40, 48, 57, 69, 81, 97, 113, 134, 157, 184, 214, 250, 290, 337, 389, 451, 519, 598, 688, 789, 904, 1035, 1181, 1348, 1535, 1746, 1983, 2250, 2549, 2885, 3261, 3682, 4154, 4680, 5268, 5923, 6656, 7468
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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This is also the inverted graded generating function for the number of partitions in which no square parts are present
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REFERENCES
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Noureddine Chair, Partition Identities From Partial Supersymmetry, hep-th/0409011 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)^k*x^k^2).
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EXAMPLE
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E.g."a(10)=8 because 10=8+2=7+3=6+4=5+3+2=6+2+2=4+2+2+2=2+2+2+2+2."
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MAPLE
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series(product((1+x^k)/(1-(-1)^k*x^(k^2)), k=1..100), x=0, 100);
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CROSSREFS
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Sequence in context: A081360 A117409 A092833 this_sequence A157046 A017979 A140881
Adjacent sequences: A100923 A100924 A100925 this_sequence A100927 A100928 A100929
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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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