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A177547
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Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, up, up, up.
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2
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1, 1, 2, 6, 24, 120, 720, 5020, 40000, 358560, 3571200, 39124800, 467612575, 6054492822, 84421683166, 1261227594360, 20098408531680, 340297488208325, 6100696794591542, 115446620042888642, 2299637587367422120, 48097983978364729800, 1053895947990450296810
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OFFSET
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0,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..175
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FORMULA
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a(n) ~ c * d^n * n!, where d = 0.995974410535227680608696027123957375635061175769113923461462667..., c = 1.0246396933863574062731686342310661124393526441879248790690509... . - Vaclav Kotesovec, Jan 17 2015
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MAPLE
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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, 1, 3, 3, 3][t]), j=1..u)+
add(b(u+j-1, o-j, [2, 2, 4, 5, 6, 7][t]), j=1..o)))
end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25); # Alois P. Heinz, Oct 23 2013
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MATHEMATICA
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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, 1, 3, 3, 3}[[t]]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, {2, 2, 4, 5, 6, 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 *)
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CROSSREFS
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Columns k=47,61 of A242784.
Sequence in context: A324138 A324137 A177552 * A324136 A177548 A193935
Adjacent sequences: A177544 A177545 A177546 * A177548 A177549 A177550
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, May 10 2010
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EXTENSIONS
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a(17)-a(22) from Alois P. Heinz, Oct 23 2013
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STATUS
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approved
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