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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
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OFFSET
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0,33
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LINKS
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FORMULA
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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
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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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MATHEMATICA
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T[n_, m_] := T[n, m] = Which[n==m, 1, m<n/2 || m>n, 0, True, Sum[T[n-m, i], {i, 0, m-1}]];
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CROSSREFS
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Row sums = A088567. Rows read from right to left also give (essentially) A088567.
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KEYWORD
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AUTHOR
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STATUS
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approved
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