A368923 - OEIS

%I #44 Aug 06 2024 09:57:48

%S 2,2,5,5,13,8,16,11,19,14,22,17,25,20,28,23,31,26,34,29,37,32,40,35,

%T 43,38,46,41,49,44,52,47,55,50,58,53,61,56,64,59,67,62,70,65,73,68,76,

%U 71,79,74,82,77,85,80,88,83,91,86,94,89,97,92,100,95,103,98,106,101,109

%N Number of congruences of the 0-twisted Brauer monoid of degree n.

%H Paolo Xausa, <a href="/A368923/b368923.txt">Table of n, a(n) for n = 0..10000</a>

%H J. East and N. Ruškuc, <a href="https://doi.org/10.1016/j.aim.2021.108097">Classification of congruences of twisted partition monoids</a>, Advances in Mathematics, 395 (2022); <a href="https://arxiv.org/abs/2010.04392">arXiv version</a>, arXiv:2010.04392 [math.RA], 2020.

%H J. East, J. Mitchell, N. Ruškuc and M. Torpey, <a href="https://doi.org/10.1016/j.aim.2018.05.016">Congruence lattices of finite diagram monoids</a>, Advances in Mathematics, 333 (2018), 931-1003; <a href="https://arxiv.org/abs/1709.00142">arXiv version</a>, arXiv:1709.00142 [math.GR], 2018.

%H Matthias Fresacher, <a href="https://www.youtube.com/watch?v=kEovBqAQxPU">Congruence Lattices of Finite Twisted Brauer Monoids</a>, youtube video (2023).

%H Matthias Fresacher, <a href="https://www.youtube.com/watch?v=YPiSVZY1z7k">(10min B&TL) Congruence Lattices of Finite Twisted Brauer & Temperley-Lieb Monoids-MatthiasFresacher</a>, youtube video (2024).

%H Matthias Fresacher, <a href="https://www.youtube.com/watch?v=X9hDw0vNxYA">(50min B&TL) Congruence Lattices of Finite Twisted Brauer & Temperley-Lieb Monoids-MatthiasFresacher</a>, youtube video (2024).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F a(n) = (3*n + 1)/2 if n is odd.

%F a(n) = (3*n + 14)/2 if n is even and n >= 4.

%F a(n) = a(n-2) + 3 for n >= 5.

%F G.f.: -(5*x^5-5*x^4-x^2-2)/((x+1)*(x-1)^2).

%F a(n) = A147677(n+1) for n >= 3.

%t LinearRecurrence[{1, 1, -1}, {2, 2, 5, 5, 13, 8}, 100] (* _Paolo Xausa_, Feb 27 2024 *)

%Y Essentially the same as A147677.

%Y Cf. A008585.

%Y Closely related to A373011.

%K easy,nonn

%O 0,1

%A _Matthias Fresacher_, Jan 09 2024