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A177526
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Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, down.
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2
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1, 1, 2, 6, 24, 120, 680, 4480, 33600, 285434, 2684680, 27812170, 313926560, 3842611240, 50625902600, 714873188122, 10764733339179, 172258243070682, 2918333808555034, 52191694000877878, 982479378895814520, 19419959862935129834, 402131210857811703926
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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 = 0.94123983763344712685016041467..., c = 1.3558011859159420827133973526... . - 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=0, 1,
add(b(u-j, o+j-1, [1, 3, 4, 1, 6][t]), j=1..u)+
add(b(u+j-1, o-j, [2, 2, 2, 5, 2][t]), j=1..o)))
end:
a:= n-> `if`(n=0, 1, add(b(j-1, n-j, 1), j=1..n)):
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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, 3, 4, 1, 6}[[t]]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 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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