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A177532
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Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, up, up.
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2
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1, 1, 2, 6, 24, 120, 701, 4774, 37128, 326089, 3184221, 34191983, 400308461, 5076257396, 69329710171, 1014612340743, 15838898430094, 262706269352374, 4613506518038420, 85520547931176984, 1668736482655334275, 34189755475407632542, 733851215342599413848
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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 = 0.975638124670183802889377522566191208591041394..., c = 1.123281860028517266849117754708517961017398615... . - Vaclav Kotesovec, Jan 17 2015
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MAPLE
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b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o+t<6, (u+o)!,
add(b(u-j, o+j-1, [1, 1, 4, 1, 1][t]), j=1..u)+
add(b(u+j-1, o-j, [2, 3, 3, 5, 6][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 > 5, 0, If[u + o + t < 6, (u + o)!,
Sum[b[u - j, o + j - 1, {1, 1, 4, 1, 1}[[t]]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, {2, 3, 3, 5, 6}[[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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