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A328507 Number of inversion sequences of length n avoiding the consecutive pattern 101.

%I A328507 #22 Aug 21 2020 17:31:05
%S A328507 1,1,2,6,23,109,619,4113,31352,269841,2589026,27404677,317265161,
%T A328507 3988181568,54099618419,787705115000,12253696410675,202831037178017,
%U A328507 3559585021719875,66018657264425355,1290284788431977106,26505045303122642171,570918508059059670322
%N A328507 Number of inversion sequences of length n avoiding the consecutive pattern 101.
%H A328507 Alois P. Heinz, <a href="/A328507/b328507.txt">Table of n, a(n) for n = 0..250</a>
%H A328507 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 A328507 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 A328507 a(n) ~ n! * c / sqrt(n), where c = 2.48988835987151440021135203237... - _Vaclav Kotesovec_, Oct 19 2019
%p A328507 b:= proc(n, j, t) option remember; `if`(n=0, 1, add(
%p A328507       `if`(i<=j or i<>t, b(n-1, i, j), 0), i=1..n))
%p A328507     end:
%p A328507 a:= n-> b(n, 0$2):
%p A328507 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 18 2019
%t A328507 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 A328507 a[n_] := b[n, 0, 0];
%t A328507 a /@ Range[0, 25] (* _Jean-François Alcover_, Mar 19 2020, after _Alois P. Heinz_ *)
%Y A328507 Cf. A049774, A052169, A071075, A200404.
%K A328507 nonn
%O A328507 0,3
%A A328507 _Vaclav Kotesovec_ and _Juan S. Auli_, Oct 17 2019