%I #7 Aug 01 2012 03:17:59
%S 0,2,1,2,4,3,1,3,2,2,4,3,4,6,5,3,5,4,1,3,2,3,5,4,2,4,3,2,4,3,4,6,5,3,
%T 5,4,4,6,5,6,8,7,5,7,6,3,5,4,5,7,6,4,6,5,1,3,2,3,5,4,2,4,3,3,5,4,5,7,
%U 6,4,6,5,2,4,3,4,6,5,3,5,4,2,4,3,4,6,5,3,5,4,4,6,5,6,8,7,5,7,6,3,5,4,5,7,6
%N Row sums of triangle A120854, which is the matrix log of triangle A117939.
%C Triangle A117939 is related to powers of 3 partitions of n and is the matrix square of A117947(n,k) = balanced ternary digits of C(n,k) mod 3, also A117947(n,k) = L(C(n,k)/3) where L(j/p) is the Legendre symbol of j and p.
%F a(n) = 2*A062756 + A081603(n), where A062756(n) = number of 1's in ternary expansion of n and A081603(n) = number of 2's in ternary expansion of n.
%t f[n_] := DigitCount[n, 3] /. {a_, b_, c_} -> 2a + b + 0c; Array[f, 105, 0] (* _Robert G. Wilson v_, Jul 31 2012 *)
%o (PARI) {a(n)=local(M=matrix(n+1,n+1,r,c,(binomial(r-1,c-1)+1)%3-1)^2, L=sum(i=1,#M,-(M^0-M)^i/i));return(sum(k=0,n,L[n+1,k+1]))}
%Y Cf. A120854, A117947; A062756, A081603, A053735.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jul 08 2006