

A221877


Number of orderpreserving or orderreversing full contraction mappings (of an nchain) 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
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OFFSET

1,2


COMMENTS

Row sums are A221882.


REFERENCES

A. D. Adeshola, V. Maltcev and A. Umar, Combinatorial results for certain semigroups of orderpreserving 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(nk+1)*C(n1,k1) if k > 1.


EXAMPLE

T (3,2) = 8 because there are exactly 8 orderpreserving full contraction mappings (of a 3chain) 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



