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Search: id:A134979
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| A134979 |
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Triangle read by rows: T(n,k) = number of partitions of n where the maximum number of objects in partitions of any given size is k. |
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| 1, 0, 2, 0, 1, 2, 0, 1, 1, 3, 0, 0, 3, 2, 2, 0, 0, 2, 4, 1, 4, 0, 0, 1, 6, 3, 3, 2, 0, 0, 1, 6, 4, 6, 1, 4, 0, 0, 0, 6, 7, 8, 3, 3, 3, 0, 0, 0, 5, 7, 14, 4, 6, 2, 4, 0, 0, 0, 0, 0, 0, 5, 7, 18, 7, 9, 5, 3, 2, 0, 0, 0, 3, 10, 22, 9, 14, 6, 6, 1, 6, 0, 0, 0, 2, 9, 26, 15, 19, 11, 9, 3, 5, 2
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Every column is eventually 0; the last row with a non-zero value in column k is A024916(k). T(A024916(k)-i, k) <= P(i), where P is the partition function (A000041); equality holds for 0 <= i <= k. The partition represented by the last number in column k is row k of A010766.
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EXAMPLE
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For the partition [3,2^2], there are 3 objects in the part of size 3, and 4 objects in the parts of size 2, so this partition is counted towards T(7,4).
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CROSSREFS
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Cf. A008284, A091602, A000041 (row sums), A000005 (main diagonal), A032741 (2nd diagonal), A010766.
Adjacent sequences: A134976 A134977 A134978 this_sequence A134980 A134981 A134982
Sequence in context: A115723 A114525 A127672 this_sequence A112248 A010872 A025858
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KEYWORD
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nonn,tabl
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AUTHOR
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Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Feb 04 2008, corrected Feb 06 2008
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