If $T_n$ is the amount of numbers with maximum $n$ digits (in base 5), that do not have a 21 sequence find a recurrence relation for $T_n$.
My solution is $T_n = 5T_{n-1} - T_{n-2}$;$T_0 = 1 , T_1 = 5$
I also tested this for n=2 and n=3, but I'm still not sure if this is correct (since I find contradicting results for n=4)
Can someone confirm if this is correct? Thanks!