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A177550
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Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, up, down, down.
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2
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1, 1, 2, 6, 24, 120, 720, 4950, 38880, 343440, 3369600, 36352800, 427680000, 5452027218, 74846801304, 1100895311340, 17272089457920, 287920937620800, 5081935953473280, 94681381716805374, 1856848184953043760, 38236452673395920040, 824863858830361247040
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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 = 0.98057763883233672986361278986560196505968263650602..., c = 1.129827226571293707156672292645277720979050046894688... . - 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, [1, 1, 4, 1, 6, 7][t]), j=1..u)+
add(b(u+j-1, o-j, [2, 3, 3, 5, 3, 2][t]), j=1..o)))
end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25); # Alois P. Heinz, Oct 29 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, {1, 1, 4, 1, 6, 7}[[t]]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, {2, 3, 3, 5, 3, 2}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 19 2022, after Alois P. Heinz *)
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CROSSREFS
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Column k=52 of A242784.
Sequence in context: A189285 A177545 A177538 * A177536 A177549 A177542
Adjacent sequences: A177547 A177548 A177549 * A177551 A177552 A177553
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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(17)-a(22) from Alois P. Heinz, Oct 29 2013
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STATUS
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approved
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