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binary pascalish triangle
Posted:
Mar 6, 2012 1:49 PM



Every row in this triangle is a power of 3 in binary
1 11 101 11011 101001 1111011 101110001 10001010011
In the second column from the left, 1010100..., there are no consecutive 1s. I want to know what the ratio of 0s to 1s converges to, if it converges.
On the right side of the triangle, there are the patterns 1111..., then 101010..., then 1000... which are powers of 3 modulo powers of 2. Is there any quicker way to find the nth pattern than modular arithmetic?



