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A177542
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Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, down, down.
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2
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1, 1, 2, 6, 24, 120, 720, 4976, 39296, 349056, 3444480, 37382400, 442506240, 5674931536, 78376004800, 1159755383520, 18305304913920, 306984257241600, 5451042337781760, 102170107109747648, 2015786374006453760, 41759419845040968960, 906291283573022730240
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ c * d^n * n!, where d = 0.9864854125625269564394281614736489845203102136102401801..., c = 1.08769348749685060865572679319744616257509477068722272... . - 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, 5, 6, 7][t]), j=1..u)+
add(b(u+j-1, o-j, [2, 2, 4, 2, 4, 2][t]), j=1..o)))
end:
a:= n-> b(n, 0, 1):
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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, 5, 6, 7}[[t]]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, {2, 2, 4, 2, 4, 2}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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