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A177538
Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, down, down.
2
1, 1, 2, 6, 24, 120, 720, 4941, 38736, 341496, 3354939, 36244098, 427006404, 5448087216, 74864913552, 1102353646680, 17314190063037, 288936154260522, 5105249306345502, 95216905474054011, 1869347069817467076, 38535066745735462848, 832195054189721911392
OFFSET
0,3
LINKS
FORMULA
a(n) ~ c * d^n * n!, where d = 0.98162590771907099517875504406285427992737137228..., c = 1.1133866874983726502599853171771818959460675... . - 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, 3, 4, 1, 6, 7][t]), j=1..u)+
add(b(u+j-1, o-j, [2, 2, 2, 5, 2, 2][t]), j=1..o)))
end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25); # Alois P. Heinz, Oct 22 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, 3, 4, 1, 6, 7}[[t]]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 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=36,54 of A242784.
Sequence in context: A189848 A189285 A177545 * A177550 A177536 A177549
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 10 2010
EXTENSIONS
a(17)-a(22) from Alois P. Heinz, Oct 22 2013
STATUS
approved