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A338738
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Number of permutations p of [n] such that |p(i) - p(i-1)| <= |p(i+1) - p(i)|.
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2
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1, 1, 2, 4, 6, 8, 10, 14, 20, 24, 32, 40, 48, 70, 94, 126, 162, 228, 292, 386, 528, 710, 956, 1298, 1730, 2342, 3178, 4192, 5684, 7720, 10340, 14002, 18816, 25372, 34054
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OFFSET
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0,3
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LINKS
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EXAMPLE
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a(4) = 6: 1234, 2314, 2341, 3214, 3241, 4321.
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MAPLE
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b:= proc(s, x, y) option remember; `if`(s={}, 1, add(
`if`(x=0 or y=0 or abs(x-y)<=abs(y-j),
b(s minus {j}, y, j), 0), j=s))
end:
a:= n-> b({$1..n}, 0$2):
seq(a(n), n=0..16);
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MATHEMATICA
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b[s_, x_, y_] := b[s, x, y] = If[s == {}, 1, Sum[If[x == 0 || y == 0 || Abs[x - y] <= Abs[y - j], b[s ~Complement~ {j}, y, j], 0], {j, s}]];
a[n_] := b[Range[n], 0, 0];
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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