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A102381
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.
3
1, 2, 6, 8, 60, 24, 504, 576, 6480, 5760, 242352, 93312, 6200064, 5612544, 95294880, 136249344, 13687492608, 5022425088, 693149184000, 472559616000, 18501259714560, 23441203298304, 4435759798272000, 1568692666368000, 262234601210880000, 317576826394214400
OFFSET
1,2
COMMENTS
a(n) = n*A086595(n).
EXAMPLE
a(4)=8 because we have 1234, 1432, 2143, 2341, 3214, 3412, 4123 and 4321.
MAPLE
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);
MATHEMATICA
{1}~Join~Array[Count[Permutations@ Range@ #, w_ /; AllTrue[Map[ RotateLeft[w, #][[1 ;; 2]] &, w], CoprimeQ @@ # &]] &, 8, 2] (* Michael De Vlieger, Sep 25 2017 *)
CROSSREFS
Sequence in context: A204546 A192534 A053938 * A075998 A361296 A007849
KEYWORD
nonn
AUTHOR
Emeric Deutsch (in collaboration with Ray Chandler, Vladeta Jovovic, Leroy Quet, Zak Seidov, and Joshua Zucker), Apr 09 2005
EXTENSIONS
a(15) and a(16) from Ray Chandler and Joshua Zucker, Apr 12 2005
a(17)-a(24) from Max Alekseyev, Jun 13 2005
a(25)-a(26) (using A086595) from Alois P. Heinz, May 05 2023
STATUS
approved