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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; refs; listen; history; internal format)
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OFFSET
| 0,25
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LINKS
| Index entries for sequences related to partitions
Henry Bottomley, Partition calculators using java applets
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FORMULA
| 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
| 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
| 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 * A014081 A091890 A029431
Adjacent sequences: A070933 A070934 A070935 * A070937 A070938 A070939
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KEYWORD
| nonn,tabl
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), May 12 2002
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