A221881 Number of order-preserving or order-reversing full contraction mappings (of an n-chain) with (right) waist exactly k.

1, 1, 3, 1, 5, 7, 1, 7, 13, 15, 1, 9, 21, 29, 31, 1, 11, 31, 51, 61, 63, 1, 13, 43, 83, 113, 125, 127, 1, 15, 57, 127, 197, 239, 253, 255, 1, 17, 73, 185, 325, 437, 493, 509, 511, 1, 19, 91, 259, 511, 763, 931, 1003, 1021, 1023

Offset

1,3

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 2013).

Links

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

Formula

T(n,k) = 2*Sum_{p=1..k} C(n-1,p-1) - 1 for k >=1.

Example

T(5,2) = 9 because there are exactly 9 order-preserving or order-reversing full contraction mappings (of a 5-chain) with (right) waist exactly 2, namely: (11112), (11122), (11222), (12222), (21111), (22111), (22211), (22221), (22222).

Crossrefs

Cf. A221876, A221877, A221878, A221879, A221880, A221882.

Sequence in context: A038871 A209819 A193648 * A201811 A199898 A320904

Adjacent sequences: A221878 A221879 A221880 * A221882 A221883 A221884

Keyword

nonn,tabl

Author

Abdullahi Umar, Feb 28 2013

Status

approved