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A177541
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Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, up, up.
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2
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1, 1, 2, 6, 24, 120, 720, 4990, 39520, 352080, 3484800, 37936800, 450606300, 5797965980, 80341280840, 1192794269400, 18889568419200, 317838157969125, 5662578565559400, 106488682710940108, 2107992477960872320, 43815112964794432080, 954074378001971825930
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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 = 0.98977300089321592191180343193285102663621683..., c = 1.06422234334396404091033045795479059186356... . - 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=0, 1,
add(b(u-j, o+j-1, [1, 3, 4, 1, 3, 3][t]), j=1..u)+
add(b(u+j-1, o-j, [2, 2, 2, 5, 6, 7][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 > 6, 0, If[u + o + t < 7, (u + o)!,
Sum[b[u - j, o + j - 1, {1, 3, 4, 1, 3, 3}[[t]]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 6, 7}[[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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