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A279571 Number of length n inversion sequences avoiding the patterns 100, 101, and 201. 22
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..25.

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-Fran├žois Alcover, Oct 27 2017, after Alois P. Heinz *)

CROSSREFS

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.

Sequence in context: A130579 A279570 A107945 * A014330 A225294 A124294

Adjacent sequences:  A279568 A279569 A279570 * A279572 A279573 A279574

KEYWORD

nonn

AUTHOR

Megan A. Martinez, Feb 21 2017

EXTENSIONS

a(10)-a(25) from Alois P. Heinz, Feb 22 2017

STATUS

approved

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Last modified February 27 12:47 EST 2020. Contains 332306 sequences. (Running on oeis4.)