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A250262
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Number of permutations p of [n] such that p(i) > p(i+1) iff i == 1 (mod 6).
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2
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1, 1, 1, 2, 3, 4, 5, 6, 41, 208, 711, 1970, 4741, 10284, 123397, 1041224, 5690415, 24359248, 87922385, 278723178, 4777712981, 56439873880, 424119250083, 2456329637366, 11821181689417, 49308397822776, 1098781192727401, 16688667550625072, 159609583197355203
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OFFSET
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0,4
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LINKS
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MAPLE
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b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
`if`(t=1, add(b(u-j, o+j-1, irem(t+1, 6)), j=1..u),
add(b(u+j-1, o-j, irem(t+1, 6)), j=1..o)))
end:
a:= n-> b(0, n, 0):
seq(a(n), n=0..35);
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MATHEMATICA
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b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1, If[t == 1, Sum[b[u - j, o + j - 1, Mod[t + 1, 6]], {j, 1, u}], Sum[b[u + j - 1, o - j, Mod[t + 1, 6]], {j, 1, o}]]];
a[n_] := b[0, n, 0];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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