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A177535
Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, down, up.
2
1, 1, 2, 6, 24, 120, 720, 5011, 39856, 356616, 3545280, 38768400, 462487631, 5977005477, 83186290826, 1240460869290, 19730730733920, 333451122953921, 5966845400766578, 112703780178989573, 2240828272067529040, 46780834679854338540, 1023129822229674425971
OFFSET
0,3
LINKS
FORMULA
a(n) ~ c * d^n * n!, where d = 0.9941229421721758523485136789468386588070503717223814960732680334748287519..., c = 1.036291721564809563490641628457988175489113294377683691938047314400726... . - 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, 5, 6, 1][t]), j=1..u)+
add(b(u+j-1, o-j, [2, 2, 2, 2, 2, 7][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, 5, 6, 1}[[t]]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, {2, 2, 2, 2, 2, 7}[[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
Column k=33 of A242784.
Sequence in context: A177537 A177541 A177551 * A263929 A324139 A324138
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 10 2010
EXTENSIONS
a(17)-a(22) from Alois P. Heinz, Oct 22 2013
STATUS
approved