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URL: https://oeis.org/A393341

⇱ A393341 - OEIS


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A393341
Number of Cayley permutations of size n avoiding 123 and 321.
3
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
OFFSET
0,3
COMMENTS
Has a set of horizontal insertion encodings which form a regular language.
LINKS
Christian Bean, Paul C. Bell, and Abigail Ollson, The insertion encoding of Cayley permutations, arXiv:2505.08480 [math.CO], 2025.
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
a(n) = 6*2^n-n-7-3*n^2, n>0. - R. J. Mathar, Feb 24 2026
CROSSREFS
Cf. A007583, A393343, A393344 also representing Cayley permutations avoiding two size 3 patterns.
Sequence in context: A005422 A040017 A007615 * A065540 A084171 A192875
KEYWORD
nonn,easy
AUTHOR
Abigail Ollson, Feb 12 2026
STATUS
approved