

A184050


T(n,k) is the number of orderpreserving and orderdecreasing partial isometries (of an nchain) 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
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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 orderdecreasing partial isometries of a finite chain, arXiv:1101.2558.


FORMULA

T(n,0)= A000325(n1) and T(n,k)=C(n,k), (k>0)


EXAMPLE

T (4,2) = 6 because there are exactly 6 orderpreserving and orderdecreasing partial isometries (on a 4chain) 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 coordinatewise


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



