Hemachandra

"The sum of the last and the one before the last is the number ... of the next mātrā-vṛtta."

"The number of combinations for matra meters are stated [as follows]. The sum (योगः) of the last and last-but-one (अन््त्ययौपान््ततौ) terms is the number of meters possible for a given number of matras."

"Hence, the sum of 2 and 1 is three, which is the number of meters with 3 matras."

"The sum of 3 and 2 is five, which is the number of meters with 4 matras."

"The sum of 5 and 3 is eight, which is the number of meters with 5 matras."

"The sum of 8 and 5 is thirteen, which is the number of meters with 6 matras."

"The sum of 13 and 8 is twenty-one, which is the number of meters with 7 matras."

"Likewise, 34, which is the sum of 21 and 13, is the number of meters with 8 matras. [Hence you have the sequence] 1, 2, 3, 5, 8, 13, 21, 34, ..."