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A221877 Number of order-preserving or order-reversing full contraction mappings (of an n-chain) with height exactly k. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 30 06:13 EDT 2022. Contains 357099 sequences. (Running on oeis4.)