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A189358
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Number of permutations p of 1,2,...,n satisfying |p(i+1)-p(i)|<>3 and |p(j+3)-p(j)|<>1 for all i=1..n-1, j=1..n-3.
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10
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1, 1, 2, 6, 8, 24, 126, 524, 3072, 22854, 189646, 1827114, 19889946, 238648524, 3131979014, 44540692612, 681114241416, 11136984461270
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OFFSET
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0,3
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COMMENTS
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a(n) is also the number of ways to place n nonattacking pieces rook + leaper[1,3] on an n X n chessboard (in fairy chess the leaper[1,3] is called a camel).
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LINKS
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FORMULA
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Asymptotic: a(n)/n! ~ 1/e^4.
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MATHEMATICA
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A189358[n_] := Module[{p, c = 0, i = 1, q},
p=Permutations[Range[n]]; While[i <= Length[p], q = p[[i]]; i++;
If[AllTrue[Range[n - 1], Abs[q[[# + 1]] - q[[#]]] != 3 &] &&
AllTrue[Range[n - 3], Abs[q[[# + 3]] - q[[#]]] != 1 &], c++]]; c];
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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