The Naraya cow sequence, named after the 14th-century Indian mathematician Narayana Pandita, considers a herd that begins with one cow in the first year and in which each cow gives birth to one calf a year from the age of three onwards. The sequence for years n = 1, 2, ... then gives 1, 1, 1 + 1 cow born = 2, 2 + 1 cow born = 3, 3 + 1 cow born = 4, 4 + 2 cows born = 6, and so one. Continuing gives the sequence 1, 1, 2, 3, 4, 6, 9, 13, 19, 28, 41, 60, ... (OEIS A000930). The n th Narayana cow number N_n gives the number of integer compositions of n involving only 1 and 3, the first few of which are shown in the following table.

Narayana number | Narayana triangle | supergolden ratio