A120855 Row sums of triangle A120854, which is the matrix log of triangle A117939.

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, 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, 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

Offset

0,2

Comments

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.

Links

Table of n, a(n) for n=0..104.

Formula

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.

Mathematica

f[n_] := DigitCount[n, 3] /. {a_, b_, c_} -> 2a + b + 0c; Array[f, 105, 0] (* Robert G. Wilson v, Jul 31 2012 *)

Prog

(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]))}

Crossrefs

Cf. A120854, A117947; A062756, A081603, A053735.

Sequence in context: A201908 A337712 A256184 * A193737 A160001 A339549

Adjacent sequences: A120852 A120853 A120854 * A120856 A120857 A120858

Keyword

nonn

Author

Paul D. Hanna, Jul 08 2006

Status

approved