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%I #29 Mar 02 2023 15:24:14
%S 1,1,1,3,5,15,31,93,215,653,1619,4979,12949,40293,108517,341241,
%T 943937,2996127,8465319,27092419,77878271,251073791,732129719,
%U 2375764351,7012025277,22886955207,68254122669,223946197065,673885100857,2221505541773,6737598265009
%N Number of idempotents in the Kauffman monoid K_n.
%C The elements of K_n are pairs (i,alpha) where i is a nonnegative integer, and alpha is an element of the Jones monoid J_n. The product in K_n is defined in the Borisavljevic-Došen-Petrić article below.
%C Also the number of idempotent basis elements of the Temperley-Lieb algebra in the case the twisting parameter is not an M-th root of unity where M <= n.
%H Mirjana Borisavljević, Kosta Došen, and Zoran Petrić, <a href="https://arxiv.org/abs/math/0008187">Kauffman monoids</a>, arXiv:math/0008187 [math.GT], 2000-2001; J. Knot Theory Ramifications, 11(2):127-143, 2002.
%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.
%H James D. Mitchell, <a href="https://github.com/james-d-mitchell/Jones">C++ code to compute the sequence</a>
%Y Cf. A225798, A281442.
%K nonn
%O 0,4
%A _James East_, Oct 05 2017