The following are a subset of the run-maximal strings for rho_2(69)

aababbabaababbababbabaababbabaababbababbabaababbababbabaababbabaababb
aababbabaababbabaababaababbabaababbababbabaababbabaababaababbabaababb
aababbabaababbababbabaababbababbabbababbabaababbababbabaababbababbabb