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Search: id:A087897
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| A087897 |
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Number of partitions of n into odd parts greater than 1. |
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+0
3
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| 1, 0, 0, 1, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 6, 8, 8, 10, 12, 13, 15, 18, 20, 23, 27, 30, 34, 40, 44, 50, 58, 64, 73, 83, 92, 104, 118, 131, 147, 166, 184, 206, 232, 256, 286, 320, 354, 394, 439, 485, 538, 598, 660, 730, 809, 891, 984, 1088, 1196, 1318, 1454, 1596, 1756
(list; graph; listen)
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OFFSET
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0,10
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COMMENT
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Also number of partitions of n into distinct parts which are not powers of 2.
Also number of partitions of n into distinct parts such that the two largest parts differ by 1.
Also number of partitions of n such that the largest part occurs an odd number of times that is at least 3 and every other part occurs an even number of times. Example: a(10)=2 because we have [2,2,2,1,1,1,1] and [2,2,2,2,2]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
Also difference between number of partitions of 1+n into distinct parts and number of partitions of n into distinct parts. - Philippe LALLOUET (philip.lallouet(AT)wanadoo;.r), May 08 2007
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REFERENCES
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R. K. Guy, Two theorems on partitions, Math. Gaz., 42 (1958), 84-86. Math. Rev. 20 #3110.
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FORMULA
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G.f.: Product_{k >= 1} 1/(1-x^(2*k+1)).
G.f.: Product_{k >= 1, k not a power of 2} (1+x^k).
G.f.=sum(x^(3k)/product(1-x^(2j), j=1..k), k=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
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EXAMPLE
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a(10)=2 because we have [7,3] and [5,5].
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MAPLE
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To get 128 terms: t4 := mul((1+x^(2^n)), n=0..7); t5 := mul((1+x^k), k=1..128): t6 := series(t5/t4, x, 100); t7 := seriestolist(t6);
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CROSSREFS
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Cf. A000009.
Sequence in context: A053251 A090184 A029057 this_sequence A029056 A036847 A029055
Adjacent sequences: A087894 A087895 A087896 this_sequence A087898 A087899 A087900
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Dec 04 2003
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