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A328433 Number of inversion sequences of length n avoiding the consecutive patterns 011 and 012. 16
1, 1, 2, 4, 11, 37, 157, 791, 4676, 31490, 238814, 2009074, 18585645, 187366675, 2045016693, 24018394333, 302051731428, 4049206907012, 57642586053512, 868375941780450, 13801973373609889, 230808858283551859, 4051069379668626948, 74459335679007458268 (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 011 and 012.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..464

Juan S. Auli and Sergi Elizalde, Consecutive patterns in inversion sequences II: avoiding patterns of relations, arXiv:1906.07365 [math.CO], 2019.

FORMULA

a(n) ~ n! * c * (3^(3/2)/(2*Pi))^n / n^alfa, where alfa = A073016 = Sum_{k>=1} 1/binomial(2*k, k) = 1/3 + 2*Pi/3^(5/2) = 0.73639985871871507790... and c = 2.21611825460684222558745179... - Vaclav Kotesovec, Oct 19 2019

EXAMPLE

The a(4)=11 length 4 inversion sequences avoiding the consecutive patterns 011 and 012 are 0000, 0100, 0010, 0020, 0001, 0101, 0021, 0002, 0102, 0003, 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, A328430, A328431, A328432, A328434, A328435, A328436, A328437, A328438, A328439, A328440, A328441, A328442.

Sequence in context: A281481 A138301 A173939 * A118182 A179327 A107107

Adjacent sequences:  A328430 A328431 A328432 * A328434 A328435 A328436

KEYWORD

nonn

AUTHOR

Juan S. Auli, Oct 16 2019

STATUS

approved

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