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Search: id:A059607
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| A059607 |
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As an upper right triangle, number of distinct partitions of n where the highest part is k (0<=k<=n). |
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4
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| 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 2, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 2, 3, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 2, 3, 3, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 1, 3, 4, 3, 2, 2, 1, 1, 1
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OFFSET
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0,33
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FORMULA
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T(n, k) =sum_j[T(n-k, j)] for k>j with T(0, 0)=1
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EXAMPLE
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Rows are {1,0,0,0,...}, {1,0,0,0,...}, {1,1,0,0,...}, {1,1,1,1,...}, {1,1,1,2,...} etc. T(7,4)=2 since 7 can be written as 4+3 or 4+2+1. T(12,6)=3 since 12 can be written as 6+5+1 or 6+4+2 or 6+3+2+1.
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CROSSREFS
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As upper right triangle, row sum is A011782, column sum is A000009, column maximum is A025591 (offset), row maximum is A026839 (offset). Cf. A026836 for this triangle starting at (1, 1) rather than (0, 0).
Sequence in context: A086009 A086010 A089198 this_sequence A015318 A026836 A089052
Adjacent sequences: A059604 A059605 A059606 this_sequence A059608 A059609 A059610
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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), Jan 30 2001
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