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A328429 Number of inversion sequences of length n avoiding the consecutive patterns 012, 101, 102, and 201.

%I A328429 #18 Jun 01 2022 01:55:10
%S A328429 1,1,2,5,14,46,170,691,3073,14809,76666,423886,2490514,15479614,
%T A328429 101389508,697513653,5025406212,37819960947,296618360520,
%U A328429 2419362514273,20484053318220,179723185666151,1631519158000420,15302546831928727,148099068509673563
%N A328429 Number of inversion sequences of length n avoiding the consecutive patterns 012, 101, 102, and 201.
%C A328429 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}. This is the same as the set of inversion sequences of length n avoiding the consecutive patterns 012, 101, 102, and 201.
%H A328429 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.
%e A328429 The a(4)=14 length 4 inversion sequences avoiding the consecutive patterns 012, 101, 102, and 201 are 0000, 0100, 0010, 0110, 0020, 0001, 0011, 0111, 0021, 0002, 0112, 0022, 0003, and 0113.
%p A328429 # after _Alois P. Heinz_ in A328357
%p A328429 b := proc(n, x, t) option remember; `if`(n = 0, 1, add(
%p A328429        `if`(t and i <> x, 0, b(n-1, i, i<x)), i=0 .. n - 1))
%p A328429      end proc:
%p A328429 a := n -> b(n, -1, false):
%p A328429 seq(a(n), n = 0 .. 24);
%t A328429 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 A328429 a[n_] := b[n, -1, False];
%t A328429 a /@ Range[0, 24] (* _Jean-François Alcover_, Mar 02 2020 after _Alois P. Heinz_ in A328357 *)
%Y A328429 Cf. A328357, A328358, A328430, A328431, A328432, A328433, A328434, A328435, A328436, A328437, A328438, A328439, A328440, A328441, A328442.
%K A328429 nonn
%O A328429 0,3
%A A328429 _Juan S. Auli_, Oct 15 2019