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A279571 Number of length n inversion sequences avoiding the patterns 100, 101, and 201.

%I A279571 #20 Oct 09 2021 02:10:14
%S A279571 1,1,2,6,22,92,424,2106,11102,61436,353980,2110366,12955020,81569168,
%T A279571 525106698,3447244188,23028080268,156246994264,1075127143948,
%U A279571 7492458675666,52820934349420,376331681648402,2707312468516446,19650530699752470,143807774782994412,1060472244838174574,7875713244761349666,58876660310205135380,442862775457168812898,3350397169412102710198
%N A279571 Number of length n inversion sequences avoiding the patterns 100, 101, and 201.
%C A279571 A length n inversion sequence e_1e_2...e_n is a sequence of integers where 0 <= e_i <= i-1. The term a(n) counts those length n inversion sequences with no entries e_i, e_j, e_k (where i<j<k) such that e_i > e_j <= e_k and e_i >= e_k. This is the same as the set of length n inversion sequences avoiding 100, 101, and 201.
%H A279571 Vaclav Kotesovec, <a href="/A279571/b279571.txt">Table of n, a(n) for n = 0..32</a>
%H A279571 Megan A. Martinez, Carla D. Savage, <a href="https://arxiv.org/abs/1609.08106">Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations</a>, arXiv:1609.08106 [math.CO], 2016.
%e A279571 The length 4 inversion sequences avoiding (100,101,201) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0102, 0103, 0110, 0111, 0112, 0113, 0120, 0121, 0122, 0123.
%p A279571 b:= proc(n, i, s, m) option remember;
%p A279571       `if`(n=0, 1, add(b(n-1, i+1, s minus {$j..m-
%p A279571       `if`(j=m, 1, 0)} union {i+1}, max(m, j)), j=s))
%p A279571     end:
%p A279571 a:= n-> b(n, 1, {1}, 0):
%p A279571 seq(a(n), n=0..15);  # _Alois P. Heinz_, Feb 22 2017
%t A279571 b[n_, i_, s_, m_] := b[n, i, s, m] = If[n == 0, 1, Sum[b[n-1, i+1, s  ~Complement~ Range[j, m - If[j == m, 1, 0]] ~Union~ {i+1}, Max[m, j]], {j, s}]];
%t A279571 a[n_] := b[n, 1, {1}, 0];
%t A279571 Table[a[n], {n, 0, 15}] (* _Jean-François Alcover_, Oct 27 2017, after _Alois P. Heinz_ *)
%Y A279571 Cf. A000108, A057552, A108307, A117106, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279572, A279573.
%K A279571 nonn
%O A279571 0,3
%A A279571 _Megan A. Martinez_, Feb 21 2017
%E A279571 a(10)-a(25) from _Alois P. Heinz_, Feb 22 2017
%E A279571 a(26)-a(29) from _Vaclav Kotesovec_, Oct 07 2021