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A328439 Number of inversion sequences of length n avoiding the consecutive pattern 011.

%I A328439 #15 Aug 21 2020 17:33:39
%S A328439 1,1,2,5,17,75,407,2621,19524,165090,1561900,16345264,187452475,
%T A328439 2337729329,31497068553,455930417721,7056447326642,116279714536838,
%U A328439 2032547040624336,37563420959431569,731810131489893185,14989602024463575408,322032777284323744894,7240745954488939549295
%N A328439 Number of inversion sequences of length n avoiding the consecutive pattern 011.
%C A328439 A length n inversion sequence e_1e_2...e_n is a sequence of integers such that 0 <= e_i < i. The term a(n) counts the inversion sequences of length n with no entries e_i, e_{i+1}, e_{i+2} such that e_i < e_{i+1} = e_{i+2}. That is, a(n) counts the inversion sequences of length n avoiding the consecutive pattern 011.
%H A328439 Vaclav Kotesovec, <a href="/A328439/b328439.txt">Table of n, a(n) for n = 0..448</a>
%H A328439 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 A328439 Juan S. Auli and Sergi Elizalde, <a href="https://arxiv.org/abs/1904.02694">Consecutive Patterns in Inversion Sequences</a>, arXiv:1904.02694 [math.CO], 2019.
%H A328439 Juan S. Auli and Sergi Elizalde, <a href="https://arxiv.org/abs/1906.07365">Consecutive patterns in inversion sequences II: avoiding patterns of relations</a>, arXiv:1906.07365 [math.CO], 2019.
%F A328439 a(n) ~ n! * c / sqrt(n), where c = 1.3306953765239857433314976921138998977998... - _Vaclav Kotesovec_, Oct 19 2019
%e A328439 The a(4)=17 length 4 inversion sequences avoiding the consecutive pattern 011 are 0000, 0100, 0010, 0020, 0120, 0001, 0101, 0021, 0121, 0002, 0102, 0012, 0003, 0103, 0013, 0023, and 0123.
%p A328439 # after _Alois P. Heinz_ in A328357
%p A328439 b := proc(n, x, t) option remember; `if`(n = 0, 1, add(
%p A328439        `if`(t and i < x, 0, b(n - 1, i, i = x)), i = 0 .. n - 1))
%p A328439      end proc:
%p A328439 a := n -> b(n, -1, false):
%p A328439 seq(a(n), n = 0 .. 24);
%t A328439 b[n_, x_, t_] := b[n, x, t] = If[n == 0, 1, Sum[If[t && i < x, 0, b[n - 1, i, i == x]], {i, 0, n - 1}]];
%t A328439 a[n_] := b[n, -1, False];
%t A328439 a /@ Range[0, 24] (* _Jean-François Alcover_, Mar 02 2020, after _Alois P. Heinz_ in A328357 *)
%Y A328439 Cf. A328357, A328358, A328429, A328430, A328431, A328432, A328433, A328434, A328435, A328436, A328437, A328438, A328440, A328441, A328442.
%K A328439 nonn
%O A328439 0,3
%A A328439 _Juan S. Auli_, Oct 17 2019