OFFSET
0,1
COMMENTS
Row sums are (1, 0, 1, 0, 0, 0, ...) with g.f. 1 + x^2.
Diagonal sums are A117907.
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
G.f.: (1 -x*(1-y) +x^2*y^2 -x^3*y -x^5*y^2)/(1-x^3*y^3).
EXAMPLE
Triangle begins
1;
-1, 1;
0, 0, 1;
0, -1, 0, 1;
0, 0, 0, -1, 1;
0, 0, -1, 0, 0, 1;
0, 0, 0, 0, -1, 0, 1;
0, 0, 0, 0, 0, 0, -1, 1;
0, 0, 0, 0, 0, -1, 0, 0, 1;
0, 0, 0, 0, 0, 0, 0, -1, 0, 1;
0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1;
0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1;
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1;
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1;
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1;
MATHEMATICA
M[n_, k_]:= M[n, k]= If[k>n, 0, If[Abs[JacobiSymbol[Binomial[n, 2], 3] - JacobiSymbol[Binomial[k, 2], 3]]==0, 1, 0]];
m:= m= With[{q=20}, Table[M[n, k], {n, 0, q}, {k, 0, q}]];
T[n_, k_]:= Inverse[m][[n+1, k+1]];
Table[T[n, k], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Oct 20 2021 *)
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Apr 01 2006
STATUS
approved