|
Search: id:A058241
|
|
|
| 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). |
|
+0
1
|
|
| 1, 1, 1, 2, 1, 5, 0, 6, 4, 6, 0, 18, 0, 20, 0, 0, 6, 51, 0, 42
(list; graph; listen)
|
|
|
OFFSET
|
1,4
|
|
|
COMMENT
|
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.
|
|
LINKS
|
Math. Archives, UBASIC
N. Nomoto, UBASIC program -> maen.zip (Maen.ub) (for n=12 it takes 30 minutes)
Eric Weisstein's World of Mathematics, Perfect Difference Set
|
|
EXAMPLE
|
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.
|
|
CROSSREFS
|
Sequence in context: A021469 A090985 A011131 this_sequence A021827 A131915 A078036
Adjacent sequences: A058238 A058239 A058240 this_sequence A058242 A058243 A058244
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Naohiro Nomoto (6284968128(AT)geocities.co.jp), Jan 16 2001
|
|
EXTENSIONS
|
More terms from Rustem Aidagulov (rustem53(AT)mail.ru), Sep 06 200 and Jan 01 2006
|
|
|
Search completed in 0.002 seconds
|
