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A279571
Number of length n inversion sequences avoiding the patterns 100, 101, and 201.
23
1, 1, 2, 6, 22, 92, 424, 2106, 11102, 61436, 353980, 2110366, 12955020, 81569168, 525106698, 3447244188, 23028080268, 156246994264, 1075127143948, 7492458675666, 52820934349420, 376331681648402, 2707312468516446, 19650530699752470, 143807774782994412, 1060472244838174574, 7875713244761349666, 58876660310205135380, 442862775457168812898, 3350397169412102710198
OFFSET
0,3
COMMENTS
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.
LINKS
Megan A. Martinez, Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016.
EXAMPLE
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.
MAPLE
b:= proc(n, i, s, m) option remember;
`if`(n=0, 1, add(b(n-1, i+1, s minus {$j..m-
`if`(j=m, 1, 0)} union {i+1}, max(m, j)), j=s))
end:
a:= n-> b(n, 1, {1}, 0):
seq(a(n), n=0..15); # Alois P. Heinz, Feb 22 2017
MATHEMATICA
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}]];
a[n_] := b[n, 1, {1}, 0];
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Oct 27 2017, after Alois P. Heinz *)
KEYWORD
nonn
AUTHOR
Megan A. Martinez, Feb 21 2017
EXTENSIONS
a(10)-a(25) from Alois P. Heinz, Feb 22 2017
a(26)-a(29) from Vaclav Kotesovec, Oct 07 2021
STATUS
approved