## Look and say sequence

### Problem 419

Published on Saturday, 16th March 2013, 10:00 pm; Solved by 281
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