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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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4
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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;
text;
internal format)
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OFFSET
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0,25
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LINKS
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Seiichi Manyama, Antidiagonals n = 0..139, flattened
Henry Bottomley, Partition calculators using java applets
Index entries for sequences related to partitions
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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: A129753 A307247 A147693 * A014081 A091890 A029431
Adjacent sequences: A070933 A070934 A070935 * A070937 A070938 A070939
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KEYWORD
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nonn,tabl,look
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AUTHOR
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Henry Bottomley, May 12 2002
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STATUS
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approved
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