A368923 - OEIS

A368923

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

2, 2, 5, 5, 13, 8, 16, 11, 19, 14, 22, 17, 25, 20, 28, 23, 31, 26, 34, 29, 37, 32, 40, 35, 43, 38, 46, 41, 49, 44, 52, 47, 55, 50, 58, 53, 61, 56, 64, 59, 67, 62, 70, 65, 73, 68, 76, 71, 79, 74, 82, 77, 85, 80, 88, 83, 91, 86, 94, 89, 97, 92, 100, 95, 103, 98, 106, 101, 109

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

Paolo Xausa, Table of n, a(n) for n = 0..10000

J. East and N. Ruškuc, Classification of congruences of twisted partition monoids, Advances in Mathematics, 395 (2022); arXiv version, arXiv:2010.04392 [math.RA], 2020.

J. East, J. Mitchell, N. Ruškuc and M. Torpey, Congruence lattices of finite diagram monoids, Advances in Mathematics, 333 (2018), 931-1003; arXiv version, arXiv:1709.00142 [math.GR], 2018.

Matthias Fresacher, Congruence Lattices of Finite Twisted Brauer Monoids, youtube video (2023).

Matthias Fresacher, (10min B&TL) Congruence Lattices of Finite Twisted Brauer & Temperley-Lieb Monoids-MatthiasFresacher, youtube video (2024).

Matthias Fresacher, (50min B&TL) Congruence Lattices of Finite Twisted Brauer & Temperley-Lieb Monoids-MatthiasFresacher, youtube video (2024).

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

FORMULA

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

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

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

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

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

MATHEMATICA

LinearRecurrence[{1, 1, -1}, {2, 2, 5, 5, 13, 8}, 100] (* Paolo Xausa, Feb 27 2024 *)