A221877 Number of order-preserving or order-reversing full contraction mappings (of an n-chain) with height exactly k.

1, 2, 2, 3, 8, 2, 4, 18, 12, 2, 5, 32, 36, 16, 2, 6, 50, 80, 60, 20, 2, 7, 72, 150, 160, 90, 24, 2, 8, 98, 252, 350, 280, 126, 28, 2, 9, 128, 392, 672, 700, 448, 168, 32, 2, 10, 162, 576, 1176, 1512, 1260, 672, 216, 36, 2

Offset

1,2

Comments

Row sums are A221882.

References

A. D. Adeshola, V. Maltcev and A. Umar, Combinatorial results for certain semigroups of order-preserving full contraction mappings of a finite chain, (submitted).

Links

Table of n, a(n) for n=1..55.

Formula

T(n,1) = n and T(n,k) = 2(n-k+1)*C(n-1,k-1) if k > 1.

Example

T (3,2) = 8 because there are exactly 8 order-preserving full contraction mappings (of a 3-chain) with exactly height 2, namely: (112), (122), (211), (221), (223), (233), (322), (332).

Crossrefs

Cf. A221876, A221878, A221879, A221880, A221881, A221882.

Sequence in context: A139073 A329955 A099870 * A110985 A153216 A327259

Adjacent sequences: A221874 A221875 A221876 * A221878 A221879 A221880

Keyword

nonn

Author

Abdullahi Umar, Feb 28 2013

Status

approved