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 = 10¹². Give your answer modulo 2³⁰ and separate your values for A, B and C by a comma. E.g. for n = 40 the answer would be 31254,20259,11625

Written by gamwe6 who lives and works in San Francisco building useful things. You should follow him on Twitter