A326308 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, 1, 3, 6, 26, 85, 476, 2171, 14905, 87153, 708825, 5053464, 47514180, 399542814, 4264132468, 41306091312, 493337571005, 5408829555639, 71476985762027, 874870165668858, 12673922434134249, 171294209823727623, 2699365743596908540, 39925463781029750810

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..486

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 / (Pi^n * sqrt(n)), where c = 1.0215796642504649172542599982453320786973706265645819484... - Vaclav Kotesovec, Oct 31 2019

Example

a(6) = 26: 010101, 010102, 010103, 010104, 010105, 010201, 010202, 010203, 010204, 010205, 010212, 010213, 010214, 010215, 010301, 010302, 010303, 010304, 010305, 010312, 010313, 010314, 010315, 010323, 010324, 010325.

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, Feb 29 2020, after Alois P. Heinz *)

Crossrefs

Cf. A000108, A000142, A000225, A001250, A328357, A328358, A328409, A328425, A328491, A326412.

Sequence in context: A260666 A140644 A321651 * A073901 A116381 A176120

Adjacent sequences: A326305 A326306 A326307 * A326309 A326310 A326311

Keyword

nonn

Author

Alois P. Heinz, Oct 17 2019

Status

approved