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A102381
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Number of permutations of 1..n in which every pair of adjacent numbers as well as the first and the last entries are relatively prime.
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3
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1, 2, 6, 8, 60, 24, 504, 576, 6480, 5760, 242352, 93312, 6200064, 5612544, 95294880, 136249344, 13687492608, 5022425088, 693149184000, 472559616000, 18501259714560, 23441203298304, 4435759798272000, 1568692666368000
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OFFSET
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1,2
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COMMENTS
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a(n)=n*A086595(n).
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LINKS
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Table of n, a(n) for n=1..24.
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EXAMPLE
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a(4)=8 because we have 1234, 1432, 2143, 2341, 3214, 3412, 4123 and 4321.
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MAPLE
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with(combinat): for n from 1 to 7 do P:=permute(n): ct:=0: for j from 1 to n! do if add(gcd(P[j][i+1], P[j][i]), i=1..n-1)=n-1 and gcd(P[j][1], P[j][n])=1 then ct:=ct+1 else ct:=ct fi od: a[n]:=ct: od: seq(a[n], n=1..7);
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MATHEMATICA
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{1}~Join~Array[Count[Permutations@ Range@ #, w_ /; AllTrue[Map[ RotateLeft[w, #][[1 ;; 2]] &, w], CoprimeQ @@ # &]] &, 8, 2] (* Michael De Vlieger, Sep 25 2017 *)
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CROSSREFS
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Cf. A086595, A076220.
Sequence in context: A204546 A192534 A053938 * A075998 A007849 A100621
Adjacent sequences: A102378 A102379 A102380 * A102382 A102383 A102384
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (in collaboration with Ray Chandler, Vladeta Jovovic, Leroy Quet, Zak Seidov, and Joshua Zucker), Apr 09 2005
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EXTENSIONS
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a(15) and a(16) from Ray Chandler and Joshua Zucker, Apr 12 2005
a(17)-a(24) from Max Alekseyev, Jun 13 2005
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STATUS
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approved
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