Sum of Binomial Coefficient with N changing exponentially and Fixed K

Question

Hello Mathematical Community, I need your help.I want to calculate sum of Binomial Coefficients where N is varying and K is fixed.

What I need to calculate is the below function :-` $$ f(n) = \sum_{i=0}^n {a^i \choose k} $$

for eg- if N = 4, a = 3, and k = 2 I need to calculate

$ ~^{3^0}C_2 + ^{3^1}C_2 + ^{3^2}C_2+ ^{3^3}C_2+ ^{3^4}C_2 = ~^{1}C_2 + ^{3}C_2 + ^{9}C_2+ ^{27}C_2+ ^{81}C_2~$

Points to Note -

1. N is rising exponentially
2. K is fixed
3. Need to calculate the sum for a particular value of N, a and k as listed in the expression above.

I have read so much about the Binomial Coefficient but couldn't find any formula or pattern from which I can derive a relation.

Any help would be nice. Thank you guys for keeping mathematicians motivated.