Here’s a much simpler way to arrive at the same number as ferrouslepidoptera:

- There are
*a*_{1} = 12 melodies of length 1, where each melody is a single note of length 1.
- There are
*a*_{2n} = 12 + *a*_{n}^{2} melodies of length 2*n*, where each melody is either a single note of length 2*n*, or the concatenation of two melodies of length *n*.
- Therefore, there are
*a*_{32} = 12 + (12 + (12 + (12 + (12 + 12^{2})^{2})^{2})^{2})^{2}
= 123,511,210,975,209,861,511,554,928,715,787,036
melodies of length 32.