CarwilBJ’s Twitter Archive

…in reply to @ilana_horn
@ilana_horn Yes, they have been generalized… Two approaches are: 1. if the nth triangle is square, so is the 4n(n+1)th triangle. See if your son can prove that. This leads up through T1=1 T8=36 T288=41616
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…in reply to @CarwilBJ
@ilana_horn 2. Less obvious but still true: The side/root of the square number are related by U(n) = 6U(n-1) - U(n-2) Starting with U(0)=0, U(1)=1. Then 6=6*1-0 35=6*6 - 1 204=6*35-6 So, next up: 6*204 - 35 = 1189 1189*2 = T1681
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