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A230832
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Number of permutations of [n] with exactly one occurrence of the consecutive step pattern up, down, up, down.
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2
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0, 0, 0, 0, 0, 16, 192, 1472, 12800, 132352, 1366016, 14781952, 178102272, 2282645504, 30639611904, 440041603072, 6720063012864, 107722700685312, 1818098902499328, 32319047553515520, 601556224722337792, 11702621573275975680, 237913839294912397312
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OFFSET
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0,6
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..460
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FORMULA
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a(n) ~ c * d^n * n! * n, where d = 0.87361286073825385348141673848..., c = 0.2252746... . - Vaclav Kotesovec, Aug 28 2014
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EXAMPLE
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a(5) = 16: 13254, 14253, 14352, 15243, 15342, 23154, 24153, 24351, 25143, 25341, 34152, 34251, 35142, 35241, 45132, 45231.
a(6) = 192: 124365, 125364, 125463, ..., 635241, 645132, 645231.
a(7) = 1472: 1235476, 1236475, 1236574, ..., 7635241, 7645132, 7645231.
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MAPLE
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b:= proc(u, o, t) option remember; `if`(t=9, 0,
`if`(u+o=0, `if`(t>4, 1, 0),
add(b(u-j, o+j-1, [1, 3, 1, 5, 7, 9, 7, 5][t]), j=1..u)+
add(b(u+j-1, o-j, [2, 2, 4, 2, 6, 8, 8, 8][t]), j=1..o)))
end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);
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MATHEMATICA
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b[u_, o_, t_] := b[u, o, t] = If[t == 9, 0,
If[u + o == 0, If[t > 4, 1, 0],
Sum[b[u - j, o + j - 1, {1, 3, 1, 5, 7, 9, 7, 5}[[t]]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, {2, 2, 4, 2, 6, 8, 8, 8}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
a /@ Range[0, 25] (* after Alois P. Heinz *)
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CROSSREFS
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Column k=1 of A230797.
Sequence in context: A302298 A305773 A317122 * A305590 A232426 A317008
Adjacent sequences: A230829 A230830 A230831 * A230833 A230834 A230835
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Oct 30 2013
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STATUS
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approved
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