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A177548 Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, down, down, down. 2
1, 1, 2, 6, 24, 120, 720, 5025, 40080, 359640, 3585600, 39322800, 470448000, 6097392939, 85106238492, 1272746220570, 20302567148160, 344103461618400, 6175195781293440, 116975122363277289, 2332451810975205960, 48833870901559002540, 1071107370496773577440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..175

FORMULA

a(n) ~ c * d^n * n!, where d = 0.99698626702423025316812958090212389097043667361318991688710688185165..., c = 1.018367520648807878150063272123153629935889863110044893080319840979... . - Vaclav Kotesovec, Jan 17 2015

MAPLE

b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,

add(b(u-j, o+j-1, [1, 1, 4, 5, 6, 7][t]), j=1..u)+

add(b(u+j-1, o-j, [2, 3, 3, 2, 2, 2][t]), j=1..o)))

end:

a:= n-> b(n, 0, 1):

seq(a(n), n=0..25); # Alois P. Heinz, Oct 23 2013

MATHEMATICA

b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,

Sum[b[u - j, o + j - 1, {1, 1, 4, 5, 6, 7}[[t]]], {j, 1, u}] +

Sum[b[u + j - 1, o - j, {2, 3, 3, 2, 2, 2}[[t]]], {j, 1, o}]]];

a[n_] := b[n, 0, 1];

Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 19 2022, after Alois P. Heinz *)

CROSSREFS

Columns k=48,60 of A242784.

Sequence in context: A177552 A177547 A324136 * A193935 A177534 A164873

Adjacent sequences: A177545 A177546 A177547 * A177549 A177550 A177551

KEYWORD

nonn

AUTHOR

R. H. Hardin, May 10 2010

EXTENSIONS

a(17)-a(22) from Alois P. Heinz, Oct 23 2013

STATUS

approved

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Last modified January 26 16:14 EST 2023. Contains 359833 sequences. (Running on oeis4.)