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

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 *)

Crossrefs

Essentially the same as A147677.

Cf. A008585.

Closely related to A373011.

Sequence in context: A300436 A056504 A122205 * A338762 A364486 A178115

Adjacent sequences: A368920 A368921 A368922 * A368924 A368925 A368926

Keyword

easy,nonn

Author

Matthias Fresacher, Jan 09 2024

Status

approved