A393344 Number of Cayley permutations of size n avoiding 123 and 231.

1, 1, 3, 11, 41, 145, 483, 1531, 4677, 13925, 40775, 118255, 341481, 985561, 2850219, 8272163, 24112013, 70599373, 207603855, 612850135, 1815219633, 5391657281, 16051239923, 47872701451, 142984764501, 427536618805, 1279455739863, 3831387897791, 11478795763577, 34402698641065

Offset

0,3

Links

Abigail Ollson, Table of n, a(n) for n = 0..99

Christian Bean, Paul C. Bell, and Abigail Ollson, The insertion encoding of Cayley permutations, arXiv:2505.08480 [math.CO], 2025.

Index entries for linear recurrences with constant coefficients, signature (11,-49,113,-142,92,-24).

Formula

G.f.: (12*x^6 - 56*x^5 + 96*x^4 - 86*x^3 + 41*x^2 - 10*x + 1)/((x - 1)^2*(2*x - 1)^3*(3*x - 1)).

E.g.f.: (1 + exp(3*x) - exp(x)*(7 + 2*x) + exp(2*x)*(7 - 6*x + 2*x^2))/2. - Stefano Spezia, Feb 13 2026

2*a(n) = -2*n -7 + (n^2/2 -7/2*n +7)*2^n +3^n. - R. J. Mathar, Feb 24 2026

Crossrefs

Cf. A007583, A393341, A393343 also represent Cayley permutations avoiding two size 3 patterns.

Sequence in context: A181863 A075276 A242233 * A294504 A086972 A218348

Adjacent sequences: A393341 A393342 A393343 * A393345 A393346 A393347

Keyword

nonn,easy

Author

Abigail Ollson, Feb 12 2026

Status

approved