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A328430 Number of inversion sequences of length n avoiding the consecutive patterns 001 and 012. 15
1, 1, 2, 3, 7, 18, 70, 317, 1825, 11805, 88212, 727731, 6660103, 66377942, 718681969, 8376682083, 104703957902, 1395883946839, 19777652272297, 296686846198829, 4697959440255354, 78299282813403618, 1370127872827224359, 25114095425698971152, 481202765468970358153 (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 001 and 012.

LINKS

Table of n, a(n) for n=0..24.

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)=7 length 4 inversion sequences avoiding the consecutive patterns 001 and 012 are 0000, 0100, 0110, 0101, 0111, 0102, and 0103.

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-Fran├žois Alcover, Mar 02 2020 after _Alois P.Heinz_ in A328357 *)

CROSSREFS

Cf. A328357, A328358, A328429, A328431, A328432, A328433, A328434, A328435, A328436, A328437, A328438, A328439, A328440, A328441, A328442.

Sequence in context: A186232 A160181 A096203 * A143874 A073641 A273006

Adjacent sequences:  A328427 A328428 A328429 * A328431 A328432 A328433

KEYWORD

nonn

AUTHOR

Juan S. Auli, Oct 15 2019

STATUS

approved

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Last modified October 21 21:51 EDT 2021. Contains 348155 sequences. (Running on oeis4.)