A200404 - OEIS

%I #32 Aug 21 2020 17:34:26

%S 1,2,6,23,107,582,3622,25369,197523,1692535,15829557,160463512,

%T 1752529064,20516018396,256273980368,3402364791737,47841014687039,

%U 710242228143271,11101522062378069,182234745428876525,3134424458578405569,56371116965252450338

%N Number of permutations avoiding the pattern 143-2.

%H Vaclav Kotesovec, <a href="/A200404/b200404.txt">Table of n, a(n) for n = 1..465</a>

%H Juan S. Auli, <a href="https://search.proquest.com/openview/3f0cef1fbdb016d61e16412e4b855969/1">Pattern Avoidance in Inversion Sequences</a>, Ph. D. thesis, Dartmouth College, ProQuest Dissertations Publishing (2020), 27964164.

%H Juan S. Auli, Sergi Elizalde, <a href="https://arxiv.org/abs/1904.02694">Consecutive Patterns in Inversion Sequences</a>, arXiv:1904.02694 [math.CO], 2019. See Table 1.

%H Andrew M. Baxter and Lara K. Pudwell, <a href="http://arxiv.org/abs/1108.2642">Enumeration schemes for vincular patterns</a>, arXiv preprint arXiv:1108.2642 [math.CO], 2011-2012.

%F 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

%t 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 *)

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Nov 17 2011

%E a(11)-a(15) from _Lars Blomberg_, Apr 16 2018

%E a(16)-a(22) from _Vaclav Kotesovec_, Oct 17 2019