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A118407
Triangle, read by rows, equal to the matrix square of triangle A118404; also equals the matrix inverse of triangle A118401.
4
1, 0, 1, -2, 0, 1, 2, -2, 0, 1, 0, 2, -2, 0, 1, -2, 0, 2, -2, 0, 1, 4, -2, 0, 2, -2, 0, 1, -6, 4, -2, 0, 2, -2, 0, 1, 4, -6, 4, -2, 0, 2, -2, 0, 1, 6, 4, -6, 4, -2, 0, 2, -2, 0, 1, -20, 6, 4, -6, 4, -2, 0, 2, -2, 0, 1, 26, -20, 6, 4, -6, 4, -2, 0, 2, -2, 0, 1, -12, 26, -20, 6, 4, -6, 4, -2, 0, 2, -2, 0, 1
OFFSET
0,4
COMMENTS
This triangle has an integer matrix square-root (A118404) 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 A118404 are all different.
FORMULA
G.f.: A(x,y) = (1+x)^2/(1+x^2)/(1+2*x+2*x^2)/(1-x*y). Column g.f.: (1+x)^2/(1+x^2)/(1+2*x+2*x^2).
EXAMPLE
Triangle begins:
1;
0, 1;
-2, 0, 1;
2,-2, 0, 1;
0, 2,-2, 0, 1;
-2, 0, 2,-2, 0, 1;
4,-2, 0, 2,-2, 0, 1;
-6, 4,-2, 0, 2,-2, 0, 1;
4,-6, 4,-2, 0, 2,-2, 0, 1;
6, 4,-6, 4,-2, 0, 2,-2, 0, 1;
-20, 6, 4,-6, 4,-2, 0, 2,-2, 0, 1;
26,-20, 6, 4,-6, 4,-2, 0, 2,-2, 0, 1; ...
PROG
(PARI) {T(n, k)=polcoeff(polcoeff((1+x)^2/(1+x^2)/(1+2*x+2*x^2)/(1-x*y+x*O(x^n)), n, x)+y*O(y^k), k, y)}
CROSSREFS
Cf. A118404 (matrix square-root), A118401 (matrix inverse), A118408 (row sums), A118409 (unsigned row sums).
Sequence in context: A127793 A127771 A248806 * A101663 A284749 A062169
KEYWORD
sign,tabl
AUTHOR
Paul D. Hanna, Apr 27 2006
STATUS
approved