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A075852
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Number of permutations s of {1,2,...,n} such that |s(i)-i|>3 for each i=1,2,...,n.
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8
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1, 0, 0, 0, 0, 0, 0, 0, 1, 16, 436, 6984, 114124, 1799688, 29125117, 486980182, 8490078104, 154750897552, 2951968964768, 58917663227568, 1229367602071416, 26787823838035750, 608794318333169289, 14411810690642972432
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OFFSET
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0,10
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COMMENTS
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a(n) equals the permanent of the n X n matrix with 0's along the main diagonal, the subdiagonal, the superdiagonal, the sub-subdiagonal, the super-superdiagonal, the sub-sub-subdiagonal, the super-super-superdiagonal, and 1's everywhere else. - John M. Campbell, Jul 09 2011
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LINKS
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MAPLE
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b:= proc(s) option remember; (n-> `if`(n=0, 1, add(
`if`(abs(n-i)>3, b(s minus {i}), 0), i=s)))(nops(s))
end:
a:= n-> b({$1..n}):
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MATHEMATICA
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a[0] = 1; a[n_] := a[n] = If[n < 8, 0, SparseArray[{Band[{1, 1}] -> 0, Band[{2, 1}] -> 0, Band[{3, 1}] -> 0, Band[{4, 1}] -> 0, Band[{1, 2}] -> 0, Band[{1, 3}] -> 0, Band[{1, 4}] -> 0}, {n, n}, 1] // Permanent];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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