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A373011
Number of congruences of the 0-twisted Temperley-Lieb monoid of degree n.
2
2, 2, 3, 3, 7, 4, 8, 5, 9, 6, 10, 7, 11, 8, 12, 9, 13, 10, 14, 11, 15, 12, 16, 13, 17, 14, 18, 15, 19, 16, 20, 17, 21, 18, 22, 19, 23, 20, 24, 21, 25, 22, 26, 23, 27, 24, 28, 25, 29, 26, 30, 27, 31, 28, 32, 29, 33, 30, 34, 31, 35, 32, 36, 33, 37, 34, 38, 35
OFFSET
0,1
LINKS
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.
FORMULA
a(n) = (n + 3)/2 if n is odd.
a(n) = (n + 10)/2 if n is even and n >= 4.
a(n) = a(n-2) + 1 for n >= 5.
MATHEMATICA
LinearRecurrence[{1, 1, -1}, {2, 2, 3, 3, 7, 4}, 100] (* Paolo Xausa, Aug 07 2024 *)
PROG
(PARI) a(n)=if(n%2, (n+3)/2, n>2, n/2+5, n/2+2) \\ Charles R Greathouse IV, Aug 07 2024
CROSSREFS
Closely related to A368923.
Sequence in context: A192495 A162223 A133076 * A295510 A324520 A307737
KEYWORD
easy,nonn
AUTHOR
Matthias Fresacher, May 23 2024
STATUS
approved