Sanskrit is a language from the Indian sub-continent, spoken for over 3500 years, and is the language of many of the main texts of Hinduism and Buddhism. Roughly 2500 years ago, one of the main branches of Sanskrit poetry (Chandras, or Vedic Sanskrit) used lines of poetry with a fixed syllable length. Sanskrit, however, has two different "lengths" of syllables; one short and one long (twice as long as a short syllable). So, if you had a 5-syllable length phrase, it could be composed of these syllables 8 ways:

short-short-short-short-short short-short-short-long

short-short-long-short

short-long-short-short

long-short-short-short long-long-short

long-short-long

short-long-long

2.1. Make a table of the number of ways to compose line lengths from 2 to 7.

2.2. One of the most frequent line lengths was an 8-syllable length. List all ways to combine short and long syllable to get an 8-syllable length. (Note that one way would be long-long-long-long. Your answer should be between 30 and 40.)

2.3. Do you see a pattern in your values from 2.1 and 2.2? Make a conjecture about how the pattern will continue.

2.4. The other two frequent line lengths in Sanskrit poetry are 11 syllables and 12 syllables. Use your conjecture from 2.3 to predict how many ways there are to construct lines of 11 and 12 syllables.