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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..24.

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

Cf. A086595, A076220.

Sequence in context: A204546 A192534 A053938 * A075998 A007849 A100621

Adjacent sequences:  A102378 A102379 A102380 * A102382 A102383 A102384

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

STATUS

approved

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Last modified February 25 14:07 EST 2021. Contains 341609 sequences. (Running on oeis4.)