A221878 - OEIS

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A221878

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

1, 0, 1, 1, 2, 1, 2, 8, 2, 1, 6, 22, 5, 2, 1, 14, 57, 12, 5, 2, 1, 34, 136, 28, 12, 5, 2, 1, 78, 315, 64, 28, 12, 5, 2, 1, 178, 710, 144, 64, 28, 12, 5, 2, 1, 398, 1577, 320, 144, 64, 28, 12, 5, 2, 1, 882, 3460, 704, 320, 144, 64, 28, 12, 5, 2, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,5

COMMENTS

Its row sum is 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..66.

FORMULA

T(n,0) = T(n-1,1), T(n,1) = A059570(n) + A221876(n,1) - n and T(n,k) = A221876 if k > 1.

EXAMPLE

T (4,0) = 6 because there are exactly 6 order-preserving or order-reversing full contraction mappings (of a 4-chain) with no fixed point, namely: (2111), (3321), (3322), (4321), (4322), (4443).

Triangle:

0, 1,

1, 2, 1,

2, 8, 2, 1,

6, 22, 5, 2, 1,

14, 57, 12, 5, 2, 1,

34, 136, 28, 12, 5, 2, 1,

78, 315, 64, 28, 12, 5, 2, 1,

178, 710, 144, 64, 28, 12, 5, 2, 1,

398, 1577, 320, 144, 64, 28, 12, 5, 2, 1,

882, 3460, 704, 320, 144, 64, 28, 12, 5, 2, 1

CROSSREFS