%I A058241
%S A058241 1,1,1,2,1,5,0,6,4,6,0,18,0,20,0,0,6,51,0,42
%N A058241 For i=1 to n, c(i) is a positive integer such that c(x) != c(y) if x 
               != y; place each c(i) on the circumference of a circle at regular 
               intervals. The arrangement must be such that any sum of adjacent 
               c(i)'s is unique (these sums range from 1 to n(n-1)+1); a(n) = number 
               of ways to choose the c(i).
%C A058241 a(1)=1, a(2)=1; conjecture: for n>2, p prime, e>0, if n-1 is of the form 
               p^e then a(n)>0 else a(n)=0.
%H A058241 Math. Archives, <a href="http://archives.math.utk.edu/software/msdos/
               number.theory/ubasic/.html">UBASIC</a>
%H A058241 N. Nomoto, <a href="http://www.geocities.co.jp/Technopolis/1793/maen.zip">
               UBASIC program -> maen.zip (Maen.ub) (for n=12 it takes 30 minutes)</
               a>
%H A058241 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PerfectDifferenceSet.html">Perfect Difference Set</a>
%e A058241 For n=3: we can choose 1 for c(1), 4 for c(2), 2 for c(3). We place the 
               three numbers on the circumference: any sum of adjacent c(i) along 
               the circumference is unique. We can see the numbers from 1 to 3*(3-1)+1. 
               { 1=1, 2= 2, 3=1+2, 4=4, 5=1+4, 6=2+4, 7=1+2+4=3*(3-1)+1 .; The set 
               of c(i) which agrees with the arrangement condition is unique so 
               a(3) = 1.
%Y A058241 Sequence in context: A021469 A090985 A011131 this_sequence A021827 A131915 
               A078036
%Y A058241 Adjacent sequences: A058238 A058239 A058240 this_sequence A058242 A058243 
               A058244
%K A058241 nonn
%O A058241 1,4
%A A058241 Naohiro Nomoto (6284968128(AT)geocities.co.jp), Jan 16 2001
%E A058241 More terms from Rustem Aidagulov (rustem53(AT)mail.ru), Sep 06 200 and 
               Jan 01 2006