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A177524
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Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, down.
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2
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1, 1, 2, 6, 24, 120, 715, 4970, 39480, 352800, 3502800, 38255900, 455795100, 5883052500, 81774966000, 1217871018000, 19346879737625, 326549862671250, 5835951345093750, 110091785625495000, 2186122850020215000, 45580964489553559375, 995625115672520581250
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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..170
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FORMULA
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a(n) ~ c * d^n * n!, where d = 0.9928637443921790380857377558103269268777241137790934589694993..., c = 1.0369478195304845650491426260146999487076420703190374702807322... . - Vaclav Kotesovec, Aug 29 2014
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MAPLE
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b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o=0, 1,
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-> `if`(n=0, 1, add(b(j-1, n-j, 1), j=1..n)):
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 > 5, 0, If[u + o == 0, 1,
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_] := If[n == 0, 1, Sum[b[j - 1, n - j, 1], {j, 1, n}]];
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=16,30 of A242784.
Sequence in context: A177531 A121987 A324132 * A223905 A164872 A226437
Adjacent sequences: A177521 A177522 A177523 * A177525 A177526 A177527
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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 20 2013
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STATUS
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approved
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