A381858 a(n) is the number of permutations of [n] that avoid 312 and 4321 and whose square avoids 231.
1, 1, 2, 5, 12, 26, 56, 125, 279, 618, 1367, 3030, 6720, 14896, 33013, 73173, 162198, 359525, 796900, 1766366, 3915256, 8678393, 19236131, 42637934, 94509351, 209485238, 464335636, 1029225640, 2281335673, 5056707001, 11208471338, 24844197877, 55068541516
Offset: 0
Links
- Michael De Vlieger, Table of n, a(n) for n = 0..2893
- Kassie Archer and Noel Bourne, Pattern avoidance in compositions and powers of permutations, arXiv:2505.05218 [math.CO], 2025. See p. 8.
- Index entries for linear recurrences with constant coefficients, signature (1,1,2,3,2).
Programs
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Mathematica
LinearRecurrence[{1,1,2,3,2},{1, 1, 2, 5, 12},33] (* James C. McMahon, Mar 10 2025 *)
Formula
G.f.: 1/(1-x-x^2-2*x^3-3*x^4-2*x^5).