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A134979 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. +0
1
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)
OFFSET

1,3

COMMENT

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.

EXAMPLE

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).

CROSSREFS

Cf. A008284, A091602, A000041 (row sums), A000005 (main diagonal), A032741 (2nd diagonal), A010766.

Sequence in context: A114525 A127672 A166124 this_sequence A112248 A010872 A025858

Adjacent sequences: A134976 A134977 A134978 this_sequence A134980 A134981 A134982

KEYWORD

nonn,tabl

AUTHOR

Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Feb 04 2008, corrected Feb 06 2008

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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