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A393341

Number of Cayley permutations of size n avoiding 123 and 321.

1, 1, 3, 11, 37, 105, 263, 607, 1329, 2813, 5827, 11907, 24125, 48625, 97695, 195911, 392425, 785541, 1571867, 3144619, 6290229, 12581561, 25164343, 50330031, 100661537, 201324685, 402651123, 805304147, 1610610349, 3221222913, 6442448207, 12884898967, 25769800665

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OFFSET

0,3

COMMENTS

Has a set of horizontal insertion encodings which form a regular language.

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 (5,-9,7,-2).

FORMULA

G.f.: (4*x^4 - 2*x^3 + 7*x^2 - 4*x + 1)/((x - 1)^3*(2*x - 1)).

E.g.f.: 2 + 6*exp(2*x) - exp(x)*(7 + 4*x + 3*x^2). - Stefano Spezia, Feb 12 2026