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A089198
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Triangle read by rows: T(n,k) (n>=0, 0<=k<=n) = number of non-squashing partitions of n into distinct parts of which the greatest is k.
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0
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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, 0, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 3, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 3, 3, 2, 2, 1, 1, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,33
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LINKS
| N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, Discrete Math., 294 (2005), 259-274.
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FORMULA
| The nonzero values of T(n, m) lie within a certain cone: T(n, m) = 0 if m < n/2 or if m > n. For m <= n <= 2m, T(n, m) = sum_{i=0}^{m-1} T(n-m, i).
For m <= n <= 2m, T(n, m) = b(n-m) if n < 2m, = b(n-m) - 1 if n = 2m, where b = A088567.
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EXAMPLE
| Triangle begins:
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
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CROSSREFS
| Row sums = A088567. Rows read from right to left also give (essentially) A088567.
Sequence in context: A086072 A086009 A086010 * A059607 A176724 A015318
Adjacent sequences: A089195 A089196 A089197 * A089199 A089200 A089201
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KEYWORD
| nonn,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 10 2003
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