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A177520
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Number of permutations of 1..n avoiding adjacent step pattern up, down, up, down.
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3
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1, 1, 2, 6, 24, 104, 528, 3296, 23168, 179712, 1573632, 15207424, 158880768, 1801996288, 22088716288, 289379395584, 4040899657728, 60045059489792, 944460646318080, 15670973219667968, 273813250221277184, 5024207327266603008, 96554813072964845568
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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 = 0.87361286073825385348141673848..., c = 1.678751353034864037734331900009... . - Vaclav Kotesovec, Aug 28 2014
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MAPLE
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b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
add(b(u+j-1, o-j, `if`(t=2, 3, 1)), j=1..o) +`if`(t<3,
add(b(u-j, o+j-1, `if`(t=1, 2, 0)), j=1..u), 0))
end:
a:= n-> b(n, 0, 0):
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MATHEMATICA
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b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1,
Sum[b[u + j - 1, o - j, If[t == 2, 3, 1]], {j, 1, o}] + If[t < 3,
Sum[b[u - j, o + j - 1, If[t == 1, 2, 0]], {j, 1, u}], 0]];
a[n_] := b[n, 0, 0];
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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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