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

Author

Abdullahi Umar, Feb 28 2013

Keywords

• nonn
• tabl

Comments

Row sums are A221882.

Examples

			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).
		

Links

• A. D. Adeshola, V. Maltcev and A. Umar, Combinatorial results for certain semigroups of order-preserving full contraction mappings of a finite chain, arXiv:1303.7428 [math.CO], 2013.
• A. D. Adeshola, A. Umar, Combinatorial results for certain semigroups of order-preserving full contraction mappings of a finite chain, JMCC 106 (2017) 37-49

Crossrefs

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

Formula

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