OFFSET
0,2
COMMENTS
The index (also called "exponent" or "critical exponent") is the largest possible value of n/p, where n is the length of a subword (contiguous block) with period p.
A word is balanced if, for pairs of subwords of the same length, the number of 0's differ by at most 1.
It is known that there exist infinite balanced words with index (5+sqrt(5))/2; for example, the infinite Fibonacci word (A003849). So a(n) is positive for all n. Furthermore, (5 + sqrt(5))/2 is the minimum possible index for which there exist balanced infinite words, which accounts for its special role here.
EXAMPLE
For n=5 the 18 words are {00010, 00100, 00101, 01110, 01010, 01001} and their reversals and complements.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Oct 10 2017
STATUS
approved