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%I #22 Oct 21 2017 22:07:40
%S 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,
%T 98,0,16,0,1,196,0,522,0,148,0,19,0,1,0,1764,0,1006,0,207,0,22,0,1,
%U 1764,0,5206,0,1673,0,275,0,25,0,1
%N Triangle read by rows: T(n,r), 0 <= r <= n, is the number of idempotents of rank r in the Jones monoid J_n.
%C Values were computed using the Semigroups package for GAP.
%H Igor Dolinka, James East, Athanasios Evangelou, Desmond FitzGerald, Nicholas Ham, James Hyde, Nicholas Loughlin, <a href="https://arxiv.org/abs/1507.04838">Idempotent Statistics of the Motzkin and Jones Monoids</a>, arXiv:1507.04838 [math.CO], 2015-2016.
%F T(2n,0) = T(2n+1,1) = A001246(n). T(2n+2,2n) = A016777(n). - _Andrey Zabolotskiy_, Oct 19 2017
%Y Cf. A225798 (row sums), A281442, A289620, A001246, A016777.
%K nonn,tabl
%O 0,8
%A _James East_, Oct 05 2017