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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 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

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