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.

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

Author

Emeric Deutsch (in collaboration with Ray Chandler, Vladeta Jovovic, Leroy Quet, Zak Seidov, and Joshua Zucker), Apr 09 2005

Keywords

• nonn

Comments

a(n) = n*A086595(n).

Examples

			a(4)=8 because we have 1234, 1432, 2143, 2341, 3214, 3412, 4123 and 4321.
		

Crossrefs

Cf. A086595, A076220.

Programs

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 *)

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