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

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:
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

Crossrefs

Cf. A221876, A221877, A221879, A221880, A221881, A221882.

Sequence in context: A140894 A208747 A334729 * A219109 A137305 A282885

Adjacent sequences: A221875 A221876 A221877 * A221879 A221880 A221881

Keyword

nonn,tabl

Author

Abdullahi Umar, Feb 28 2013

Status

approved