A118401 Triangle, read by rows, equal to the matrix square of triangle A118400; also equals the matrix inverse of triangle A118407.

1, 0, 1, 2, 0, 1, -2, 2, 0, 1, 4, -2, 2, 0, 1, -6, 4, -2, 2, 0, 1, 8, -6, 4, -2, 2, 0, 1, -10, 8, -6, 4, -2, 2, 0, 1, 12, -10, 8, -6, 4, -2, 2, 0, 1, -14, 12, -10, 8, -6, 4, -2, 2, 0, 1, 16, -14, 12, -10, 8, -6, 4, -2, 2, 0, 1, -18, 16, -14, 12, -10, 8, -6, 4, -2, 2, 0, 1, 20, -18, 16, -14, 12, -10, 8, -6, 4, -2, 2, 0, 1

Offset

0,4

Comments

This triangle has an integer matrix square-root (A118400) if the main diagonal of the square-root is allowed to be signed. Even though the columns of this triangle are all the same, the columns of the matrix square-root A118400 are all different.

Links

Table of n, a(n) for n=0..90.

Formula

G.f.: A(x,y) = (1 + 2*x + 2*x^2)*(1+x^2)/(1+x)^2/(1-x*y). Column g.f.: (1 + 2*x + 2*x^2)*(1+x^2)/(1+x)^2.

Example

Triangle begins:
1;
0, 1;
2, 0, 1;
-2, 2, 0, 1;
4,-2, 2, 0, 1;
-6, 4,-2, 2, 0, 1;
8,-6, 4,-2, 2, 0, 1;
-10, 8,-6, 4,-2, 2, 0, 1;
12,-10, 8,-6, 4,-2, 2, 0, 1;
-14, 12,-10, 8,-6, 4,-2, 2, 0, 1;
16,-14, 12,-10, 8,-6, 4,-2, 2, 0, 1; ...

Prog

(PARI) {T(n, k)=polcoeff(polcoeff((1+2*x+2*x^2)*(1+x^2)/(1+x)^2/(1-x*y+x*O(x^n)), n, x)+y*O(y^k), k, y)}

Crossrefs

Cf. A118400 (matrix square-root), A118402 (row sums), A118403 (unsigned row sums), A118407 (matrix inverse).

Sequence in context: A336695 A035465 A096144 * A354786 A147767 A113678

Adjacent sequences: A118398 A118399 A118400 * A118402 A118403 A118404

Keyword

sign,tabl

Author

Paul D. Hanna, Apr 27 2006

Status

approved