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Topic: binary pascal-ish triangle
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Angela Richardson

Posts: 42
From: UK
Registered: 6/22/11
binary pascal-ish triangle
Posted: Mar 6, 2012 1:49 PM
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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?



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