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 A225798 The number of idempotents in the Jones (or Temperley-Lieb) monoid on the set [1..n]. 4
 1, 2, 5, 12, 36, 96, 311, 886, 3000, 8944, 31192, 96138, 342562, 1083028, 3923351, 12656024, 46455770, 152325850, 565212506, 1878551444, 7033866580, 23645970022, 89222991344, 302879546290, 1150480017950, 3938480377496, 15047312553918, 51892071842570, 199274492098480, 691680497233180 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The Jones monoid is the set of partitions on [1..2n] with classes of size 2, which can be drawn as a planar graph, and multiplication inherited from the Brauer monoid, which contains the Jones monoid as a subsemigroup. The multiplication is defined in Halverson and Ram. These numbers were produced using the Semigroups (2.0) package for GAP 4.7. No general formula is known for the number of idempotents in the Jones monoid. LINKS Attila Egri-Nagy, Nick Loughlin, and James Mitchell Table of n, a(n) for n = 1..30 (a(1) to a(21) from Attila Egri-Nagy, a(22)-a(24) from Nick Loughlin, a(25)-a(30) from James Mitchell) I. Dolinka, J. East, A. Evangelou, D. FitzGerald, N. Ham, et al., Enumeration of idempotents in diagram semigroups and algebras, arXiv preprint arXiv:1408.2021 [math.GR], 2014. I. Dolinka, J. East et al, Idempotent Statistics of the Motzkin and Jones Monoids, arXiv:1507.04838 [math.CO], 2015. Table 4 and 5. T. Halverson, A. Ram, Partition algebras, European J. Combin. 26 (6) (2005) 869-921. J. D. Mitchell et al., Semigroups package for GAP. PROG (GAP) for i in [1..18] do Print(NrIdempotents(JonesMonoid(i)), "\n"); od; CROSSREFS Cf. A000108, A227545, A225797. Sequence in context: A108555 A292169 A283799 * A303204 A032203 A197444 Adjacent sequences:  A225795 A225796 A225797 * A225799 A225800 A225801 KEYWORD nonn AUTHOR James Mitchell, Jul 27 2013 EXTENSIONS a(20)-a(21) from Attila Egri-Nagy, Sep 12 2014 a(22)-a(24) from Nick Loughlin, Jan 23 2015 a(25)-a(30) from James Mitchell, May 21 2016 STATUS approved

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Last modified October 19 00:36 EDT 2018. Contains 316327 sequences. (Running on oeis4.)