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A328435 Number of inversion sequences of length n avoiding the consecutive patterns 101, 102, and 201.

%I A328435 #13 Jun 01 2022 01:55:43
%S A328435 1,1,2,6,21,83,368,1814,9837,58095,370499,2534374,18493023,143280489,
%T A328435 1173971656,10136279104,91936857611,873547634921,8673546319685,
%U A328435 89796095349193,967384904147690,10825116242427973,125613702370667158,1509222589338456874,18748890945849736182
%N A328435 Number of inversion sequences of length n avoiding the consecutive patterns 101, 102, and 201.
%C A328435 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 101, 102, and 201.
%H A328435 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 A328435 Note that a(4)=21. Indeed, of the 24 inversion sequences of length 4, the only ones that do not avoid the consecutive patterns 101, 102, and 201 are 0101, 0102, and 0103.
%p A328435 # after _Alois P. Heinz_ in A328357
%p A328435 b := proc(n, x, t) option remember; `if`(n = 0, 1, add(
%p A328435        `if`(t and x < i, 0, b(n - 1, i, i < x)), i = 0 .. n - 1))
%p A328435      end proc:
%p A328435 a := n -> b(n, -1, false):
%p A328435 seq(a(n), n = 0 .. 24);
%t A328435 b[n_, x_, t_] := b[n, x, t] = If[n == 0, 1, Sum[If[t && x < i, 0, b[n - 1, i, i < x]], {i, 0, n - 1}]];
%t A328435 a[n_] := b[n, -1, False];
%t A328435 a /@ Range[0, 24] (* _Jean-François Alcover_, Mar 02 2020 after _Alois P. Heinz_ in A328357 *)
%Y A328435 Cf. A328357, A328358, A328429, A328430, A328431, A328432, A328433, A328434, A328436, A328437, A328438, A328439, A328440, A328441, A328442.
%K A328435 nonn
%O A328435 0,3
%A A328435 _Juan S. Auli_, Oct 17 2019