A393344 - OEIS

%I #13 Feb 24 2026 05:02:56

%S 1,1,3,11,41,145,483,1531,4677,13925,40775,118255,341481,985561,

%T 2850219,8272163,24112013,70599373,207603855,612850135,1815219633,

%U 5391657281,16051239923,47872701451,142984764501,427536618805,1279455739863,3831387897791,11478795763577,34402698641065

%N Number of Cayley permutations of size n avoiding 123 and 231.

%H Abigail Ollson, <a href="/A393344/b393344.txt">Table of n, a(n) for n = 0..99</a>

%H Christian Bean, Paul C. Bell, and Abigail Ollson, <a href="https://arxiv.org/abs/2505.08480">The insertion encoding of Cayley permutations</a>, arXiv:2505.08480 [math.CO], 2025.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (11,-49,113,-142,92,-24).

%F 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)).

%F 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

%F 2*a(n) = -2*n -7 + (n^2/2 -7/2*n +7)*2^n +3^n. - _R. J. Mathar_, Feb 24 2026

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

%K nonn,easy

%O 0,3

%A _Abigail Ollson_, Feb 12 2026