

A281442


Triangle read by rows: T(n,r), 0 <= r <= n, is the number of idempotents of rank r in the Kauffman monoid K_n.


3



1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 4, 0, 1, 0, 8, 0, 6, 0, 1, 0, 0, 22, 0, 8, 0, 1, 0, 42, 0, 40, 0, 10, 0, 1, 0, 0, 140, 0, 62, 0, 12, 0, 1, 0, 262, 0, 288, 0, 88, 0, 14, 0, 1, 0, 0, 992, 0, 492, 0, 118, 0, 16, 0, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,8


COMMENTS

Values were computed using the Semigroups package for GAP.
T(n,r) is also the number of idempotent basis elements of rank r in the TemperleyLieb algebra of degree n in the generic case (when the twisting parameter is not an mth root of unity for any m <= n).


LINKS

Table of n, a(n) for n=0..65.
Igor Dolinka, James East, Athanasios Evangelou, Desmond FitzGerald, Nicholas Ham, James Hyde, Nicholas Loughlin, Idempotent Statistics of the Motzkin and Jones Monoids, arXiv:1507.04838 [math.CO], 20152016.


FORMULA

T(2n1,1) = A005315(n). Empirical: T(2n,2) = A077056(n); T(n+2,n2) = 2*A028875(n) for n>2.  Andrey Zabolotskiy, Oct 19 2017


CROSSREFS

Cf. A281438 (row sums), A281441, A289620.
Sequence in context: A036852 A260941 A329918 * A256038 A050327 A075120
Adjacent sequences: A281439 A281440 A281441 * A281443 A281444 A281445


KEYWORD

nonn,tabl


AUTHOR

James East, Oct 05 2017


STATUS

approved



