

A120855


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


1



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
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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(r1, c1)+1)%31)^2, L=sum(i=1, #M, (M^0M)^i/i)); return(sum(k=0, n, L[n+1, k+1]))}


CROSSREFS

Cf. A120854, A117947; A062756, A081603, A053735.
Sequence in context: A201912 A201908 A256184 * A193737 A160001 A179750
Adjacent sequences: A120852 A120853 A120854 * A120856 A120857 A120858


KEYWORD

nonn


AUTHOR

Paul D. Hanna, Jul 08 2006


STATUS

approved



