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%I #14 Jun 01 2022 01:55:33
%S 1,1,2,5,15,53,216,994,5076,28403,172538,1129511,7919314,59150556,
%T 468504022,3919569708,34518111783,319030219223,3086250047021,
%U 31174921402976,328110078110137,3591110146030066,40800503952916639,480429785491094856,5854374278697301978
%N Number of inversion sequences of length n avoiding the consecutive patterns 010, 021, and 120.
%C 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 010, 021, and 120.
%H 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 The a(4)=15 length 4 inversion sequences avoiding the consecutive patterns 010, 021, 120 and are 0000, 0110, 0001, 0011, 0111, 0002, 0012, 0112, 0022, 0122, 0003, 0013, 0113, 0023, and 0123.
%p # after _Alois P. Heinz_ in A328357
%p b := proc(n, x, t) option remember; `if`(n = 0, 1, add(
%p `if`(t and i < x, 0, b(n - 1, i, i > x)), i = 0 .. n - 1))
%p end proc:
%p a := n -> b(n, n, false):
%p seq(a(n), n = 0 .. 24);
%t 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 a[n_] := b[n, n, False];
%t a /@ Range[0, 24] (* _Jean-François Alcover_, Mar 02 2020 after _Alois P. Heinz_ in A328357 *)
%Y Cf. A328357, A328358, A328429, A328430, A328431, A328433, A328434, A328435, A328436, A328437, A328438, A328439, A328440, A328441, A328442.
%K nonn
%O 0,3
%A _Juan S. Auli_, Oct 16 2019
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