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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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4
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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; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| 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
| Eric Weisstein's World of Mathematics, Durfee Square.
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FORMULA
| 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
| Array starts: 1; 0,1; 0,2; 0,3; 0,4,1; 0,5,2
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CROSSREFS
| For another version see A115994. Row lengths A003059.
Cf. A115721, A115722, A008284, A006918.
Sequence in context: A008801 A073739 A046767 * A053120 A008743 A029179
Adjacent sequences: A115717 A115718 A115719 * A115721 A115722 A115723
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KEYWORD
| nonn,tabf
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AUTHOR
| Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 11 2006
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