Problem 419

Look and say sequence

The **look and say** sequence goes 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ...

The sequence starts with 1 and all other members are obtained by describing the previous member in terms of consecutive digits.

It helps to do this out loud:

1 is 'one one' 11

11 is 'two ones' 21

21 is 'one two and one one' 1211

1211 is 'one one, one two and two ones' 111221

111221 is 'three ones, two twos and one one' 312211

...

Define A(n), B(n) and C(n) as the number of ones, twos and threes in the n'th element of the sequence respectively.

One can verify that A(40) = 31254, B(40) = 20259 and C(40) = 11625.

Find A(n), B(n) and C(n) for n = 10^{12}.

Give your answer modulo 2^{30} and separate your values for A, B and C by a comma.

E.g. for n = 40 the answer would be 31254,20259,11625

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These problems are part of
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