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A328504 Number of inversion sequences of length n avoiding the consecutive pattern 010.

%I A328504 #22 Aug 21 2020 17:31:22
%S A328504 1,1,2,5,17,76,417,2701,20199,171329,1624851,17036586,195685618,
%T A328504 2443572835,32959210808,477542545691,7396931591165,121976733648960,
%U A328504 2133460758692093,39450254899737811,768950119933799815,15757352298761474101,338663233082663363407
%N A328504 Number of inversion sequences of length n avoiding the consecutive pattern 010.
%H A328504 Alois P. Heinz, <a href="/A328504/b328504.txt">Table of n, a(n) for n = 0..250</a>
%H A328504 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 A328504 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 4.
%F A328504 a(n) ~ n! * c / sqrt(n), where c = 1.410641128930866501817126119... - _Vaclav Kotesovec_, Oct 19 2019
%p A328504 b:= proc(n, j, t) option remember; `if`(n=0, 1, add(
%p A328504       `if`(i>=j or i<>t, b(n-1, i, j), 0), i=1..n))
%p A328504     end:
%p A328504 a:= n-> b(n, 0$2):
%p A328504 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 18 2019
%t A328504 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 A328504 a[n_] := b[n, 0, 0];
%t A328504 a /@ Range[0, 25] (* _Jean-François Alcover_, Mar 12 2020, after _Alois P. Heinz_ *)
%Y A328504 Cf. A049774, A052169, A071075, A200404.
%K A328504 nonn
%O A328504 0,3
%A A328504 _Vaclav Kotesovec_ and _Juan S. Auli_, Oct 17 2019