

A111776


Triangle read by rows: number of idempotent orderpreserving partial transformations (of an nelement chain) of waist k (waist(alpha) = max(Im(alpha)).


2



1, 1, 1, 1, 2, 3, 1, 4, 6, 10, 1, 8, 12, 20, 35, 1, 16, 24, 40, 70, 125, 1, 32, 48, 80, 140, 250, 450, 1, 64, 96, 160, 280, 500, 900, 1625
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OFFSET

0,5


COMMENTS

G(n, n) is A081567(n  1)


REFERENCES

Laradji, A. and Umar, A. Combinatorial results for semigroups of orderpreserving partial transformations. Journal of Algebra 278, (2004), 342359.


LINKS

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


FORMULA

G(n,k)= (2^(nk))*G(n,n)=(2^(nk))*A081567(n1), G(0,0) = 1


EXAMPLE

G(3,2) = 6 because there are exactly 6 idempotent orderpreserving partial transformations (on a 3element chain) of waist 2, namely: (2)>(2), (1,2)>(1,2), (1,2)>(2,2),(1,3)>(3,3), (2,3)>(2,2), (2,3)>(3,3)  the mappings are coordinatewise


CROSSREFS

Cf. A081567.
Sequence in context: A073809 A303648 A298364 * A189187 A299714 A171083
Adjacent sequences: A111773 A111774 A111775 * A111777 A111778 A111779


KEYWORD

nonn,tabl


AUTHOR

Abdullahi Umar, Aug 25 2008


STATUS

approved



