A177471 - OEIS

%I #18 Nov 03 2020 04:57:43

%S 1,1,2,6,18,61,281,1541,8920,57924,437490,3611389,31721537,304085783,

%T 3180772870,35422074330,418050879810,5266547286061,70459362412265,

%U 991921937012273,14681437097585260,228615478225446360,3730868960721027906,63577641238069645741

%N 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.

%H Alois P. Heinz, <a href="/A177471/b177471.txt">Table of n, a(n) for n = 0..472</a>

%H S. Kitaev, <a href="https://doi.org/10.1016/j.dam.2006.09.011">Introduction to partially ordered patterns</a>, Discrete Applied Mathematics 155 (2007), 929-944.

%F a(n) ~ c * d^n * n!, where d = 0.7411900298994603810165..., c = 2.41202786457703060749584... . - _Vaclav Kotesovec_, Aug 22 2014

%p b:= proc(u, o, s, t) option remember; `if`(u+o=0, 1,

%p        add(b(u-j, o+j-1, t, false), j=1..u)+

%p       `if`(s, 0, add(b(u+j-1, o-j, t, true), j=1..o)))

%p     end:

%p a:= n-> b(n, 0, false$2):

%p seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 25 2013

%t 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}]]];

%t a[n_] := b[n, 0, False, False];

%t a /@ Range[0, 25] (* _Jean-François Alcover_, Nov 03 2020, after _Alois P. Heinz_ *)

%K nonn

%O 0,3

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

%E a(10)-a(23) from _Alois P. Heinz_, Oct 25 2013