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A184050 T(n,k) is the number of order-preserving and order-decreasing partial isometries (of an n-chain) with exactly k fixed points. 1
1, 1, 1, 2, 2, 1, 5, 3, 3, 1, 12, 4, 6, 4, 1, 27, 5, 10, 10, 5, 1, 58, 6, 15, 20, 15, 6, 1, 121, 7, 21, 35, 35, 21, 7, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..35.

R. Kehinde, S. O. Makanjuola and A. Umar, On the semigroup of order-decreasing partial isometries of a finite chain, arXiv:1101.2558.

FORMULA

T(n,0)= A000325(n-1) and T(n,k)=C(n,k), (k>0)

EXAMPLE

T (4,2) = 6 because there are exactly 6 order-preserving and order-decreasing partial isometries (on a 4-chain) of fix 2, namely: (1,2)-->(1,2); (2,3)-->(2,3); (3,4)-->(3,4); (1,3)-->(1,3); (2,4)-->(2,4); (1,4)-->(1,4) - the mappings are coordinate-wise

CROSSREFS

Row sums are A000325 for n >= 0

Sequence in context: A088333 A016538 A134226 * A324798 A226059 A127742

Adjacent sequences:  A184047 A184048 A184049 * A184051 A184052 A184053

KEYWORD

nonn,tabl

AUTHOR

Abdullahi Umar, Jan 12 2011

STATUS

approved

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Last modified November 21 09:14 EST 2019. Contains 329362 sequences. (Running on oeis4.)