A117947 T(n,k)=L(C(n,k)/3) where L(j/p) is the Legendre symbol of j and p.

1, 1, 1, 1, -1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, -1, 1, 1, -1, 1, 1, 0, 0, -1, 0, 0, 1, 1, 1, 0, -1, -1, 0, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, -1, 1, 1, -1, 1, 0, 0, 0, 1, -1, 1, 1, -1, 1

Offset: 0

Author

Paul Barry, Apr 05 2006

Keywords

• easy
• sign
• tabl

Comments

Row sums are A059126. Diagonal sums are A117963. Could be called the Legendre-binomial matrix for p=3.

The matrix square equals triangle A117939; the matrix log equals triangle A120854 divided by 2. - Paul D. Hanna, Jul 08 2006

Examples

			Triangle begins:
  1;
  1, 1;
  1, -1, 1;
  1, 0, 0, 1;
  1, 1, 0, 1, 1;
  ...
		

Crossrefs

Cf. A117939 (matrix square), A120854 (2*log).

Programs

PARI

T(n,k)=(binomial(n,k)+1)%3-1 - Paul D. Hanna, Jul 08 2006

Formula

T(n,k) = balanced ternary digit of C(n,k) mod 3. - Paul D. Hanna, Jul 08 2006