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A177534
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Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, down, down.
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2
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1, 1, 2, 6, 24, 120, 720, 5034, 40224, 361584, 3611520, 39679200, 475580160, 6175139244, 86348433264, 1293675609960, 20674025187840, 351037594569600, 6311110770685440, 119767524064039062, 2392482308124881520, 50181968955048369480, 1102681392427432825920
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OFFSET
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0,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..200
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FORMULA
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a(n) ~ c * d^n * n!, where d = 0.99880260814201465936657157017137377717606254472452619578417647021809..., c = 1.0072348951217738673562195411256011395302888145883911883919110478... . - 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+t<7, (u+o)!,
add(b(u-j, o+j-1, `if`(t=1, 1, t+1)), j=1..u)+
add(b(u+j-1, o-j, 2), j=1..o)))
end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25); # Alois P. Heinz, Oct 21 2013
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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, If[t == 1, 1, t + 1]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, 2], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 20 2022, after Alois P. Heinz *)
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CROSSREFS
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Columns k=32,62 of A242784.
Sequence in context: A324136 A177548 A193935 * A164873 A226438 A248839
Adjacent sequences: A177531 A177532 A177533 * A177535 A177536 A177537
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, May 10 2010
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EXTENSIONS
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a(18)-a(22) from Alois P. Heinz, Oct 21 2013
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STATUS
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approved
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