A281441 Triangle read by rows: T(n,r), 0 <= r <= n, is the number of idempotents of rank r in the Jones monoid J_n.

1, 0, 1, 1, 0, 1, 0, 4, 0, 1, 4, 0, 7, 0, 1, 0, 25, 0, 10, 0, 1, 25, 0, 57, 0, 13, 0, 1, 0, 196, 0, 98, 0, 16, 0, 1, 196, 0, 522, 0, 148, 0, 19, 0, 1, 0, 1764, 0, 1006, 0, 207, 0, 22, 0, 1, 1764, 0, 5206, 0, 1673, 0, 275, 0, 25, 0, 1

Offset: 0

Author

James East, Oct 05 2017

Keywords

• nonn
• tabl

Comments

Values were computed using the Semigroups package for GAP.

Links

• 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], 2015-2016.

Crossrefs

Cf. A225798 (row sums), A281442, A289620, A001246, A016777.

Formula

T(2n,0) = T(2n+1,1) = A001246(n). T(2n+2,2n) = A016777(n). - Andrey Zabolotskiy, Oct 19 2017