A200404 Number of permutations avoiding the pattern 143-2.

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

Vaclav Kotesovec, Table of n, a(n) for n = 1..465

Juan S. Auli, Pattern Avoidance in Inversion Sequences, Ph. D. thesis, Dartmouth College, ProQuest Dissertations Publishing (2020), 27964164.

Juan S. Auli, 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.

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

Adjacent sequences: A200401 A200402 A200403 * A200405 A200406 A200407

Keyword

nonn

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