A147677 -id:A147677 - cp's OEIS frontend

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

Matthias Fresacher, Jan 09 2024

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).

Essentially the same as A147677.
Cf. A008585.
Closely related to A373011.

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

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.

A168195 a(n) = 2*n - a(n-1) + 1 with n>1, a(1)=5.

Original entry on oeis.org

5, 0, 7, 2, 9, 4, 11, 6, 13, 8, 15, 10, 17, 12, 19, 14, 21, 16, 23, 18, 25, 20, 27, 22, 29, 24, 31, 26, 33, 28, 35, 30, 37, 32, 39, 34, 41, 36, 43, 38, 45, 40, 47, 42, 49, 44, 51, 46, 53, 48, 55, 50, 57, 52, 59, 54, 61, 56, 63, 58, 65, 60, 67, 62, 69, 64, 71, 66, 73

Offset: 1

Vincenzo Librandi, Nov 20 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A004442, A147677.

I:=[5,0,7]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 27 2012

A168195:=n->n+1-3*(-1)^n; seq(A168195(n), n=1..100); # Wesley Ivan Hurt, Dec 13 2013

LinearRecurrence[{1,1,-1},{5,0,7},30] (* Vincenzo Librandi, Feb 27 2012 *)

From R. J. Mathar, Nov 22 2009: (Start)
a(n) = a(n-1) + a(n-2) - a(n-3) = n + 1 - 3*(-1)^n.
G.f.: x*(5+2*x^2-5*x)/((1+x)*(x-1)^2). (End)
a(n) = n - 4 + 2^(2-(-1)^n). - Wesley Ivan Hurt, Dec 13 2013
a(n) = A004442(n-1) + 2*(1-(-1)^n) = A147677(n) - floor((n+3)/2). - Filip Zaludek, Oct 31 2016
Sum_{n>=3} (-1)^n/a(n) = 23/15 - log(2). - Amiram Eldar, Feb 23 2023

cp's OEIS Frontend

A368923 Number of congruences of the 0-twisted Brauer monoid of degree n.

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