Ternary analogue of A094913?

[Maximilian Hasler]

I offer PARI code and some values based on the reasoning found in A094913:

A094913(n,base=2)=sum(k=1,n,min(base^k,n-k+1))

vector(20,n,A094913(n))
%1 = [1, 3, 5, 8, 12, 16, 21, 27, 34, 42, 50, 59, 69, 80, 92, 105,
119, 134, 150, 166]

vector(20,n,A094913(n,3))
%2 = [1, 3, 6, 9, 13, 18, 24, 31, 39, 48, 57, 67, 78, 90, 103, 117,
132, 148, 165, 183]

M.H.