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 A227883 Number of permutations of [n] with exactly one occurrence of the consecutive step pattern up, down, up. 4
 0, 0, 0, 0, 5, 50, 328, 2154, 16751, 144840, 1314149, 12735722, 134159743, 1519210786, 18272249418, 233231701166, 3159471128588, 45243728569842, 682183513506619, 10807962134238068, 179606706777512992, 3123700853586733882, 56737351453843424893 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..460 (first 195 terms from Alois P. Heinz) FORMULA a(n) ~ c * d^n * n! * n, where d = A245758 = 0.782704180171521701844707..., c = 0.575076701401064911213333442496869737011... . - Vaclav Kotesovec, Aug 22 2014 EXAMPLE a(4) = 5: 1324, 1423, 2314, 2413, 3412. a(5) = 50: 12435, 12534, 13245, ..., 52314, 52413, 53412. MAPLE b:= proc(u, o, t) option remember;       `if`(t=7, 0, `if`(u+o=0, `if`(t in [4, 5, 6], 1, 0),       add(b(u-j, o+j-1, [1, 3, 1, 5, 6, 6][t]), j=1..u)+       add(b(u+j-1, o-j, [2, 2, 4, 4, 7, 4][t]), j=1..o)))     end: a:= n-> b(n, 0, 1): seq(a(n), n=0..25); MATHEMATICA b[u_, o_, t_] := b[u, o, t] =     If[t == 7, 0, If[u + o == 0, If[4 <= t <= 6, 1, 0],     Sum[b[u - j, o + j - 1, {1, 3, 1, 5, 6, 6}[[t]]], {j, 1, u}] +     Sum[b[u + j - 1, o - j, {2, 2, 4, 4, 7, 4}[[t]]], {j, 1, o}]]]; a[n_] := b[n, 0, 1]; a /@ Range[0, 25] (* Jean-François Alcover, Dec 20 2020, after Alois P. Heinz *) CROSSREFS Column k=1 of A227884. Cf. A177477, A245758. Sequence in context: A064054 A301821 A301997 * A227261 A036291 A060347 Adjacent sequences:  A227880 A227881 A227882 * A227884 A227885 A227886 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 25 2013 STATUS approved

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Last modified January 15 16:36 EST 2021. Contains 340187 sequences. (Running on oeis4.)