OFFSET
0,6
COMMENTS
a(n) is the number of 3-element subsets (i,j,k) of {0,...,n-1} such that k-j=j-i>0 and a(i)+a(j)=a(k). An induction argument can show simultaneously that a(n)-a(n-1) is always 0 or 1 and that the only case where three values of a(n) are equal is a(0)=a(1)=a(2)=0. Numerical evidence suggests that a(n) is asymptotic to 2n/3.
EXAMPLE
For n=9, just the triples (0,1,2),(2,3,4),(3,4,5),(4,5,6),(4,6,8) satisfy the stated conditions, so a(9) = 5
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alex Abercrombie, Jan 08 2011
STATUS
approved