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A076220 Number of permutations of 1..n in which every pair of adjacent numbers are relatively prime.

%I A076220 #28 Aug 13 2017 22:45:02
%S A076220 1,1,2,6,12,72,72,864,1728,13824,22032,555264,476928,17625600,
%T A076220 29599488,321115392,805146624,46097049600,36481536000,2754120268800,
%U A076220 3661604352000,83905105305600,192859121664000,20092043520000000,15074060547686400,1342354557616128000
%N A076220 Number of permutations of 1..n in which every pair of adjacent numbers are relatively prime.
%F A076220 a(p-1) = A086595(p) for prime p. - _Max Alekseyev_, Jun 12 2005
%e A076220 a(4) = 12 since there are 12 permutations of 1234 in which every 2 adjacent numbers are relatively prime: 1234, 1432, 2134, 2143, 2314, 2341, 3214, 3412, 4123, 4132, 4312, 4321.
%p A076220 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 then ct:=ct+1 else ct:=ct fi od: a[n]:=ct: od: seq(a[n],n=1..7); # _Emeric Deutsch_, Mar 28 2005
%p A076220 # second Maple program:
%p A076220 b:= proc(s, t) option remember; `if`(s={}, 1, add(
%p A076220       `if`(igcd(i, t)>1, 0, b(s minus {i}, i)), i=s))
%p A076220     end:
%p A076220 a:= n-> b({$1..n}, 1009):
%p A076220 seq(a(n), n=0..14);  # _Alois P. Heinz_, Aug 13 2017
%t A076220 f[n_] := Block[{p = Permutations[ Table[i, {i, 1, n}]], c = 0, k = 1}, While[k < n! + 1, If[ Union[ GCD @@@ Partition[p[[k]], 2, 1]] == {1}, c++ ]; k++ ]; c]; Do[ Print[ f[n]], {n, 2, 15}]
%o A076220 (PARI) {A076220(n)=local(A, d, n, r, M); A=matrix(n,n,i,j,if(gcd(i,j)==1,1,0)); r=0; for(s=1,2^n-1,M=vecextract(A,s,s)^(n-1);d=matsize(M)[1];r+=(-1)^(n-d)*sum(i=1,d,sum(j=1,d,M[i,j])));r} \\ _Max Alekseyev_, Jun 12 2005
%Y A076220 Cf. A086595.
%K A076220 nonn
%O A076220 0,3
%A A076220 _Lior Manor_, Nov 04 2002
%E A076220 Extended by _Frank Ruskey_, Nov 11 2002
%E A076220 a(15)-a(16) from _Ray Chandler_ and _Joshua Zucker_, Apr 10 2005
%E A076220 a(17)-a(24) from _Max Alekseyev_, Jun 12 2005
%E A076220 a(0) prepended and a(25) added by _Alois P. Heinz_, Aug 13 2017