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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. 5
1, 1, 2, 6, 18, 61, 281, 1541, 8920, 57924, 437490, 3611389, 31721537, 304085783, 3180772870, 35422074330, 418050879810, 5266547286061, 70459362412265, 991921937012273, 14681437097585260, 228615478225446360, 3730868960721027906, 63577641238069645741 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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
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

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Last modified May 21 14:18 EDT 2024. Contains 372738 sequences. (Running on oeis4.)