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A177549
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Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, down, up, up.
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2
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1, 1, 2, 6, 24, 120, 720, 4969, 39184, 347544, 3424320, 37150741, 439774085, 5639099103, 77873192126, 1152123776419, 18181366630226, 304851804959519, 5412206888619242, 101424438933572112, 2000731009697485843, 41440364401733715980, 899211137893661967405
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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..450
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FORMULA
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a(n) ~ c * d^n * n!, where d = 0.986314277283772995320277545416339641125925..., c = 1.08332315844132327949722334709840176297166... . - 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, 5, 1, 1][t]), j=1..u)+
add(b(u+j-1, o-j, [2, 3, 3, 2, 6, 7][t]), j=1..o)))
end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25); # Alois P. Heinz, Oct 23 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, 5, 1, 1}[[t]]], {j, 1, u}] + Sum[b[u+j-1, o-j, {2, 3, 3, 2, 6, 7}[[t]]], {j, 1, o}]]]; a[n_] := b[n, 0, 1]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Nov 11 2016, after Alois P. Heinz *)
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CROSSREFS
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Column k=51 of A242784.
Sequence in context: A177538 A177550 A177536 * A177542 A177537 A177541
Adjacent sequences: A177546 A177547 A177548 * A177550 A177551 A177552
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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 23 2013
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STATUS
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approved
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