A326412 Number of inversion sequences of length n where all consecutive subsequences i,j,k satisfy i >= j <= k or i <= j >= k.

1, 1, 2, 5, 17, 69, 330, 1797, 11028, 74932, 559351, 4540088, 39840318, 375421225, 3782383945, 40548234374, 460956742449, 5536790753853, 70077462043662, 931945968071778, 12993337101354500, 189485727877247991, 2884989393948284323, 45772604755492432599

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..483

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 * 2^n * n^((Pi+1)/2) / Pi^n, where c = 0.0662002484840446134... - Vaclav Kotesovec, Oct 31 2019

Example

a(4) = 17: 0000, 0001, 0002, 0003, 0010, 0011, 0020, 0021, 0022, 0100, 0101, 0102, 0103, 0110, 0111, 0112, 0113.

Maple

b:= proc(n, j, t, u, c) option remember; `if`(n=0, 1, add(
      `if`(c>0 or i>=j and t or i<=j and u, b(n-1, i,
        is(i<=j), is(i>=j), max(0, c-1)), 0), i=1..n))
    end:
a:= n-> b(n, 0, true$2, 2):
seq(a(n), n=0..25);

Mathematica

b[n_, j_, t_, u_, c_] := b[n, j, t, u, c] = If[n == 0, 1, Sum[If[c > 0 || i >= j && t || i <= j && u, b[n - 1, i, i <= j,  i >= j , Max[0, c - 1]], 0], {i, 1, n}]];
a[n_] := b[n, 0, True, True, 2];
a /@ Range[0, 25] (* Jean-François Alcover, Mar 01 2020, after Alois P. Heinz *)

Crossrefs

Cf. A000108, A000142, A000225, A001250, A328357, A328358, A328409, A328425, A328491, A326308.

Sequence in context: A303952 A162037 A319467 * A183239 A263639 A263679

Adjacent sequences: A326409 A326410 A326411 * A326413 A326414 A326415

Keyword

nonn

Author

Alois P. Heinz, Oct 17 2019

Status

approved