Cumulative Palindrome Count

Gru has been ordering the minions to do a lot of work lately. Minions don't want to trust Gru anymore. So, they propose a problem to Gru. They will only help Gru if he can answer the problem correctly. The minions generate an endless string $s$ by following these steps: 1. Let $s$ be an empty string. 2. $i = 1$. 3. Append $i$ *a* s to the back of $s$. 4. Append $i$ *b* s to the back of $s$.