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 A279567 Number of length n inversion sequences avoiding the patterns 100, 110, 120, and 210. 23
 1, 1, 2, 6, 21, 82, 343, 1509, 6893, 32419, 156058, 765578, 3815062, 19263736, 98368919, 507197436, 2637242188, 13814247530, 72834238423, 386244387688, 2058933104170, 11026807340592, 59304897232442, 320181600386661, 1734685419170666, 9428340999504441 (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= e_k and e_i > e_k. This is the same as the set of length n inversion sequences avoiding 100, 110, 120, and 210. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..400 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, 110, 120, 210) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0101, 0102, 0103, 0111, 0112, 0113, 0121, 0122, 0123. MAPLE b:= proc(n, i, m) option remember; `if`(n=0, 1, add((h->       b(n-1, i-h+1, max(m, j)-h))(max(0, min(m-1, j))), j=1..i))     end: a:= n-> b(n, 1, 0): seq(a(n), n=0..30);  # Alois P. Heinz, Feb 23 2017 MATHEMATICA b[n_, i_, m_] := b[n, i, m] = If[n == 0, 1, Sum[b[n-1, i-#+1, Max[m, j]-#]& @ Max[0, Min[m-1, j]], {j, 1, i}]]; a[n_] := b[n, 1, 0]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jul 10 2017, after Alois P. Heinz *) CROSSREFS Cf. A000108, A057552, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279568, A279569, A279570, A279571, A279572, A279573. Sequence in context: A150219 A150220 A168653 * A281784 A032347 A032346 Adjacent sequences:  A279564 A279565 A279566 * A279568 A279569 A279570 KEYWORD nonn AUTHOR Megan A. Martinez, Feb 09 2017 EXTENSIONS a(10)-a(25) from Alois P. Heinz, Feb 23 2017 STATUS approved

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Last modified February 18 00:28 EST 2020. Contains 332006 sequences. (Running on oeis4.)