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A328500 Number of inversion sequences of length n avoiding the consecutive pattern 102.

%I A328500 #25 Aug 21 2020 17:32:30
%S A328500 1,1,2,6,22,96,492,2902,19350,143918,1181540,10614698,103589738,
%T A328500 1091367634,12346368424,149276823258,1921099070062,26220186000950,
%U A328500 378308908684300,5753387612678314,91988260677198002,1542570178562361018,27072325866355742048
%N A328500 Number of inversion sequences of length n avoiding the consecutive pattern 102.
%H A328500 Alois P. Heinz, <a href="/A328500/b328500.txt">Table of n, a(n) for n = 0..250</a>
%H A328500 Juan S. Auli, <a href="https://search.proquest.com/openview/3f0cef1fbdb016d61e16412e4b855969">Pattern Avoidance in Inversion Sequences</a>, Ph. D. thesis, Dartmouth College, ProQuest Dissertations Publishing (2020), 27964164.
%H A328500 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 3.
%F A328500 a(n) ~ n! * c * d^n * n^alfa, where d = 1/A240885 = 1/(sqrt(2) * InverseErf(sqrt(2/Pi))), alfa = 0.294868853646259565..., c = 2.22826071050847602... - _Vaclav Kotesovec_, Oct 19 2019
%p A328500 b:= proc(n, j, t) option remember; `if`(n=0, 1, add(
%p A328500       `if`(i<=j or i>=t, b(n-1, i, j), 0), i=1..n))
%p A328500     end:
%p A328500 a:= n-> b(n, 0$2):
%p A328500 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 18 2019
%t A328500 b[n_, j_, t_] := b[n, j, t] = If[n == 0, 1, Sum[If[i <= j || i >= t, b[n - 1, i, j], 0], {i, 1, n}]];
%t A328500 a[n_] := b[n, 0, 0];
%t A328500 a /@ Range[0, 25] (* _Jean-François Alcover_, Mar 01 2020, after _Alois P. Heinz_ *)
%Y A328500 Cf. A049774, A071075, A200404.
%K A328500 nonn
%O A328500 0,3
%A A328500 _Vaclav Kotesovec_ and _Juan S. Auli_, Oct 17 2019