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

0,3

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.

Formula

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

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 *)

Crossrefs

Sequence in context: A228448 A346490 A177473 * A303117 A150052 A262590

Adjacent sequences: A177468 A177469 A177470 * A177472 A177473 A177474

Keyword

nonn

Author

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

Extensions

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

Status

approved