OFFSET
0,1
COMMENTS
FORMULA
Column k has g.f. (-x)^k+(x(-x)^k+x^(k+1))/2-x^(2k+2); Number triangle T(n, k)=(-1)^n*(if(n=k, 1, 0) OR if(n=2k+2, -1, 0) OR if(n=k+1, -(1+(-1)^k)/2, 0)).
G.f.: (1+x-x*y)/(1-x^2*y^2)-x^2/(1-x^2*y); - Paul Barry, Feb 02 2006
EXAMPLE
Triangle begins
1,
1, -1,
-1, 0, 1,
0, 0, 1, -1,
0, -1, 0, 0, 1,
0, 0, 0, 0, 1, -1,
0, 0, -1, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 1, -1,
0, 0, 0, -1, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 1, -1,
0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1,
0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1,
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Jan 25 2006
STATUS
approved