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A200404
Number of permutations of [n] avoiding the pattern 143-2.
6
1, 2, 6, 23, 107, 582, 3622, 25369, 197523, 1692535, 15829557, 160463512, 1752529064, 20516018396, 256273980368, 3402364791737, 47841014687039, 710242228143271, 11101522062378069, 182234745428876525, 3134424458578405569, 56371116965252450338
OFFSET
1,2
LINKS
Juan S. Auli, Pattern Avoidance in Inversion Sequences, Ph. D. thesis, Dartmouth College, ProQuest Dissertations Publishing (2020), 27964164.
Juan S. Auli and Sergi Elizalde, Consecutive Patterns in Inversion Sequences, arXiv:1904.02694 [math.CO], 2019. See Table 1.
Andrew M. Baxter and Lara K. Pudwell, Enumeration schemes for vincular patterns, arXiv preprint arXiv:1108.2642 [math.CO], 2011-2012.
Yan Wang, Qi Fang, Shishuo Fu, Sergey Kitaev, and Haijun Li, Consecutive and quasi-consecutive patterns: des-Wilf classifications and generating functions, arXiv:2502.10128 [math.CO], 2025. See p. 9.
FORMULA
a(n) ~ c * d^n * n! * n^alfa, where d = 1/A240885 = 1/(sqrt(2) * InverseErf(sqrt(2/Pi))), alfa = 0.96094544076267076286993824810734... and c = 0.5103992709959036090170192609... - Vaclav Kotesovec, Oct 17 2019
MATHEMATICA
i120[1] = 1; i120[2] = 2; i120[n_] := i120[n] = Sum[s120[n, k], {k, 0, n - 1}]; s120[n_, k_] := s120[n, k] = i120[n - 1] - Sum[(n - 2 - j)*s120[n - 2, j], {j, k + 1, n - 2}]; Table[i120[m], {m, 1, 25}] (* Vaclav Kotesovec, Oct 17 2019 *)
CROSSREFS
Sequence in context: A187761 A277176 A130908 * A000772 A200405 A336071
KEYWORD
nonn,changed
AUTHOR
N. J. A. Sloane, Nov 17 2011
EXTENSIONS
a(11)-a(15) from Lars Blomberg, Apr 16 2018
a(16)-a(22) from Vaclav Kotesovec, Oct 17 2019
STATUS
approved