%I A109813
%S A109813 1,1,2,2,12,2,72,24,144,12,22032,24,476928,480,1728,9600,805146624,720,
%T A109813 36481536000,30240,1728000,312000,192859121664000,40320,2159795404800,
%U A109813 46293120,249684249600,58423680
%N A109813 Number of permutations of (the positive integers <= n and coprime to 
               n), where each element of the permutations is coprime to its adjacent 
               elements.
%C A109813 Sequence continues: a(29) = ?, 40320, ?, 1893397524480, 32006016000000, 
               478511953920, ?, 209018880, ?, 122634632171520, ?, 665481277440, 
               ?, 399168000. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), 
               Sep 25 2006
%H A109813 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%e A109813 The integers coprime to 10 and <= 10 are (1,3,7,9).
%e A109813 Of the permutations of these integers, there are 12 permutations where 
               all adjacent terms are coprime, ie where 3 and 9 are not adjacent. 
               So the 10th term of the sequence is 12.
%o A109813 (PARI) {A109813(x)=local(v, A, d, r, M, i, j); n=eulerphi(x); v=vector(n,
               i,0); j=0; for(i=1,x,if(gcd(i,x)==1,j++;v[j]=i)); A=matrix(n, n, 
               i, j, gcd(v[i], v[j])==1); 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} - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), 
               Sep 25 2006
%Y A109813 Cf. A076220.
%Y A109813 Sequence in context: A076976 A058044 A128269 this_sequence A086595 A013605 
               A073768
%Y A109813 Adjacent sequences: A109810 A109811 A109812 this_sequence A109814 A109815 
               A109816
%K A109813 more,nonn
%O A109813 1,3
%A A109813 Leroy Quet Aug 16 2005
%E A109813 More terms from Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), 
               Sep 25 2006