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 A328436 Number of inversion sequences of length n avoiding the consecutive patterns 000 and 001. 15
 1, 1, 2, 3, 9, 37, 190, 1181, 8564, 70914, 659810, 6811371, 77232836, 953969548, 12747856402, 183218649413, 2818050980941, 46182485773217, 803323102085452, 14781372445602234, 286838921699435184, 5854404018902152208, 125367868007259046305, 2810511319383912299122 (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 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 000 and 001. LINKS Juan S. Auli and Sergi Elizalde, Consecutive patterns in inversion sequences II: avoiding patterns of relations, arXiv:1906.07365 [math.CO], 2019. EXAMPLE The a(4)=9 length 4 inversion sequences avoiding the consecutive patterns 000 and 001 are 0100, 0110, 0120, 0101, 0121, 0102, 0122, 0103, and 0123. MAPLE # after Alois P. Heinz in A328357 b := proc(n, x, t) option remember; `if`(n = 0, 1, add(        `if`(t and i = x, 0, b(n - 1, i, i <= x)), i = 0 .. n - 1))      end proc: a := n -> b(n, -1, false): seq(a(n), n = 0 .. 24); MATHEMATICA 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}]]; a[n_] := b[n, -1, False]; a /@ Range[0, 24] (* Jean-François Alcover, Mar 02 2020 after _Alois P.Heinz_ in A328357 *) CROSSREFS Cf. A328357, A328358, A328429, A328430, A328431, A328432, A328433, A328434, A328435, A328437, A328438, A328439, A328440, A328441, A328442. Sequence in context: A306523 A095412 A074428 * A125052 A181139 A162093 Adjacent sequences:  A328433 A328434 A328435 * A328437 A328438 A328439 KEYWORD nonn AUTHOR Juan S. Auli, Oct 17 2019 STATUS approved

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Last modified October 21 21:25 EDT 2021. Contains 348155 sequences. (Running on oeis4.)