A370686 a(n) is the number of 132-avoiding permutations p so that p^3 is the identity permutation.
1, 1, 1, 3, 5, 7, 17, 31, 49, 107, 201, 339, 699, 1327, 2327, 4643, 8843, 15895, 31099, 59251, 108239, 209239, 398355, 735619, 1411351, 2684147, 4993111, 9533775, 18112735, 33863375, 64457715, 122348279, 229537011, 436029791, 827012339, 1555314327, 2950532447, 5592873575, 10536068991
Offset: 0
Keywords
Links
- Kassie Archer and Robert P. Laudone, Pattern-restricted permutations of small order, arXiv:2402.15463 [math.CO], 2024.
Programs
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PARI
my(N=44,x='x+O('x^N),C(x)=(1-sqrt(1-4*x))/(2*x)); Vec(C(x^3)/(sqrt(C(x^3)*(4-3*C(x^3)))-x*C(x^3))) \\ Joerg Arndt, Feb 27 2024
Formula
G.f.: c(x^3)/(sqrt(c(x^3)*(4-3*c(x^3)))-x*c(x^3)) where c(x) is the generating function for the Catalan numbers.
Comments