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A221879
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Triangle T(n,k) read by rows: Number of order-reversing full contraction mappings (of an n-chain) with 1 fixed point and height exactly k.
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5
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1, 2, 0, 3, 2, 1, 4, 6, 4, 0, 5, 12, 12, 4, 1, 6, 20, 28, 18, 6, 0, 7, 30, 55, 52, 27, 6, 1, 8, 42, 96, 120, 88, 36, 8, 0, 9, 56, 154, 240, 230, 136, 48, 8, 1, 10, 72, 232, 434, 516, 400, 200, 60, 10, 0, 11, 90, 333, 728, 1036, 996, 650, 280, 75, 10, 1
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OFFSET
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1,2
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COMMENTS
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REFERENCES
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A. D. Adeshola, V. Maltcev and A. Umar, Combinatorial results for certain semigroups of order-preserving full contraction mappings of a finite chain, (submitted).
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LINKS
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FORMULA
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T(n, 1) = 1, T(2,2) = 0 and T(n,k) = (n-k+1)*C(n-2,k-1) + T(n-2,k-2) for k > 0.
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EXAMPLE
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T (4,6) = 6 because there are exactly 6 order-reversing full contraction mappings (of a 4-chain) with 1 fixed point and of height exactly 2, namely: (3222), (2221), (2211), (4433), (4333), (3332).
Triangle starts
1,
2, 0,
3, 2, 1,
4, 6, 4, 0,
5, 12, 12, 4, 1,
6, 20, 28, 18, 6, 0,
7, 30, 55, 52, 27, 6, 1,
8, 42, 96, 120, 88, 36, 8, 0,
9, 56, 154, 240, 230, 136, 48, 8, 1,
10, 72, 232, 434, 516, 400, 200, 60, 10, 0,
11, 90, 333, 728, 1036, 996, 650, 280, 75, 10, 1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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