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 
,
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 
th
Narayana cow number 
gives the number of integer compositions
of 
involving only 1 and 3, the first few of which are shown in the following table.
 |  | compositions of  using 1 and 3 |
| 1 | 1 | 1 |
| 2 | 1 |  |
| 3 | 2 | 3,  |
| 4 | 3 |  ,  ,  |
| 5 | 4 |  ,
 ,
 ,
 |
| 6 | 6 |  ,  ,  ,  ,  ,  |
Based on its definition, the Naraya cow sequence is evidently related to both the Fibonacci sequene and Padovan sequence.
The terms of the sequence are given by the linear recurrence
 |
(1)
|
with 
,
,
and 
.
They have generating function
 |
(2)
|
They also have a closed form in terms of a generalized hypergeometric function
 |
(3)
|
The limit of consecutive terms is the supergolden ratio
 |
(4)
|
, 
, 
, 
." Mar. 7, 2019.