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A221881 Number of order-preserving or order-reversing full contraction mappings (of an n-chain) with (right) waist exactly k. 6
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified March 25 13:31 EDT 2023. Contains 361524 sequences. (Running on oeis4.)