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

0,4

Comments

a(n) is the number of 132-avoiding permutations composed only of 3-cycles and fixed points.

Links

Table of n, a(n) for n=0..38.

Kassie Archer and Robert P. Laudone, Pattern-restricted permutations of small order, arXiv:2402.15463 [math.CO], 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.

Prog

(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

Crossrefs

Cf. A000108, A309331.

Sequence in context: A002092 A274906 A296422 * A174394 A057476 A016041

Adjacent sequences: A370683 A370684 A370685 * A370687 A370688 A370689

Keyword

nonn

Author

Kassie Archer, Feb 26 2024

Status

approved