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Search: id:A070936
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| A070936 |
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Square array read by antidiagonals: T(n,k) = number of partitions of n into distinct parts, each no more than k. |
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2
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| 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 2, 0, 0, 0, 1, 1, 1, 2, 1, 0, 0, 0, 1, 1, 1, 2, 2, 1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 1, 0, 0, 0, 1, 1, 1, 2, 2, 3, 2, 0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 2, 0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 4, 3, 1, 0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 4, 4, 3, 1, 0, 0, 0, 0
(list; table; graph; listen)
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OFFSET
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0,25
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LINKS
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Index entries for sequences related to partitions
Henry Bottomley, Partition calculators using java applets
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FORMULA
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T(n, k) =T(n-1, k)+T(n-1, k-n) (with T(0, 0)=1) =A053632(k, n) =A026836(n+k+1, k+1) =sum_{0<=j<=k}A026836(n, j). For k>=n, T(n, k)=T(n, n)=A000009(n).
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EXAMPLE
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Rows start 1,1,1,1,1,...; 0,1,1,1,1,...; 0,0,1,1,1,...; 0,0,1,2,2,...; 0,0,0,1,2,...; etc. T(10,5)=3 since 10 can be partitioned 3 ways as 5+4+1=5+3+2=4+3+2+1 with each part less than or equal to 5.
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CROSSREFS
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Cf. A008284, A060016. With some imagination, this is the transpose of A026836 and A053632. Column sums are 2^k=A000079(k). Column maximum is A025591(k), which appears A070936(k) times in the column.
Sequence in context: A089310 A129753 A147693 this_sequence A014081 A091890 A029431
Adjacent sequences: A070933 A070934 A070935 this_sequence A070937 A070938 A070939
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KEYWORD
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nonn,tabl
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), May 12 2002
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