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That is easy! substuition method, Let (x+4)/2 = pai , so x+4 = 2pai f (pai) = (2pai)^2-1

because ABBABBABBA contans three substrings ABBAs so it was included three times in the orginal count 448: ABBAxxxxxx xxxABBAxxx xxxxxxABBA we only can keep one in our counting so we have to subract two times the number of ABBABBABBA. Similiarly, strings containing two ABBAs with overlap and strings contaiinng two ABBAs without overlap were included in the orginal 448 for two times, so we only subscract once. 448-23-20-2*1 = 393 This question is a very good question to practice how to remove overcounts.