The sequence 1,3,6,10,15,dots1, 3, 6, 10, 15, \\dots1,3,6,10,15,dots (triangular numbers) has the recurrence:
an=an−1+na_n = a_{n-1} + nan=an−1+n
an=2an−1a_n = 2a_{n-1}an=2an−1
an=n2a_n = n^2an=n2
an=an−1+an−2a_n = a_{n-1} + a_{n-2}an=an−1+an−2