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A177545
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Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, up, down, down.
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2
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1, 1, 2, 6, 24, 120, 720, 4929, 38544, 338904, 3309120, 35521200, 415704960, 5271197205, 71977504692, 1053008012790, 16431803844480, 272435676775200, 4782657847248000, 88624515772410633, 1728678866577622920, 35404942557640528620, 759655818204633900000
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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 = 0.9752820884477652193970997660966130503977714987577677..., c = 1.1721546677937404500752065441275892023818795500231... . - 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, 6, 7][t]), j=1..u)+
add(b(u+j-1, o-j, [2, 2, 4, 5, 2, 4][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, 3, 6, 7}[[t]]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, {2, 2, 4, 5, 2, 4}[[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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