A177471 Avoiding the pattern 121'2'. To avoid 121'2' means not to have four consecutive letters such that the first letter is less than the second one and the third letter is less than the fourth one.

1, 1, 2, 6, 18, 61, 281, 1541, 8920, 57924, 437490, 3611389, 31721537, 304085783, 3180772870, 35422074330, 418050879810, 5266547286061, 70459362412265, 991921937012273, 14681437097585260, 228615478225446360, 3730868960721027906, 63577641238069645741

Offset: 0

Author

Signy Olafsdottir (signy06(AT)ru.is), May 09 2010

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..472
• S. Kitaev, Introduction to partially ordered patterns, Discrete Applied Mathematics 155 (2007), 929-944.

Programs

Maple

b:= proc(u, o, s, t) option remember; `if`(u+o=0, 1,
       add(b(u-j, o+j-1, t, false), j=1..u)+
      `if`(s, 0, add(b(u+j-1, o-j, t, true), j=1..o)))
    end:
a:= n-> b(n, 0, false$2):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 25 2013

Mathematica

b[u_, o_, s_, t_] := b[u, o, s, t] = If[u+o == 0, 1, Sum[b[u-j, o+j-1, t, False], {j, 1, u}] + If[s, 0, Sum[b[u+j-1, o-j, t, True], {j, 1, o}]]];
a[n_] := b[n, 0, False, False];
a /@ Range[0, 25] (* Jean-François Alcover, Nov 03 2020, after Alois P. Heinz *)

Formula

a(n) ~ c * d^n * n!, where d = 0.7411900298994603810165..., c = 2.41202786457703060749584... . - Vaclav Kotesovec, Aug 22 2014

Extensions

a(10)-a(23) from Alois P. Heinz, Oct 25 2013