The recurrence cn=3cdotcn−1c_n = 3 \\cdot c_{n-1}cn=3cdotcn−1 with c0=1c_0 = 1c0=1 has closed form:
cn=3n−1c_n = 3^{n-1}cn=3n−1
cn=n+3c_n = n + 3cn=n+3
cn=3nc_n = 3^ncn=3n
cn=ncdot3c_n = n \\cdot 3cn=ncdot3