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Search: id:A115720
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| A115720 |
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Triangle T(n,k) is the number of partitions of n with Durfee square k. |
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5
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| 1, 0, 1, 0, 2, 0, 3, 0, 4, 1, 0, 5, 2, 0, 6, 5, 0, 7, 8, 0, 8, 14, 0, 9, 20, 1, 0, 10, 30, 2, 0, 11, 40, 5, 0, 12, 55, 10, 0, 13, 70, 18, 0, 14, 91, 30, 0, 15, 112, 49, 0, 16, 140, 74, 1, 0, 17, 168, 110, 2, 0, 18, 204, 158, 5, 0, 19, 240, 221, 10, 0, 20, 285, 302, 20, 0, 21, 330, 407
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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T(n,k) is number of partitions of n-k^2 into parts of 2 kinds with at most k of each kind.
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LINKS
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Eric Weisstein's World of Mathematics, Durfee Square.
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FORMULA
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T(n,k) = Sum_{i=0}^{n-k^2} P*(i,k)*P*(n-k^2-i), where P*(n,k) = P(n+k,k) is the number of partitions of n objects into at most k parts.
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EXAMPLE
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Array starts: 1; 0,1; 0,2; 0,3; 0,4,1; 0,5,2
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CROSSREFS
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For another version see A115994. Row lengths A003059.
Cf. A115721, A115722, A008284, A006918.
Sequence in context: A008801 A073739 A046767 this_sequence A053120 A008743 A029179
Adjacent sequences: A115717 A115718 A115719 this_sequence A115721 A115722 A115723
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KEYWORD
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nonn,tabf
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 11 2006
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