OFFSET
0,1
COMMENTS
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)/((1-x^3)*(1-x^3*y^3)).
T(n, k) = [k<=n] * 2^abs(L(C(n,2)/3) - L(C(k,2)/3)) mod 2.
EXAMPLE
Triangle begins
1;
1, 1;
0, 0, 1;
1, 1, 0, 1;
1, 1, 0, 1, 1;
0, 0, 1, 0, 0, 1;
1, 1, 0, 1, 1, 0, 1;
1, 1, 0, 1, 1, 0, 1, 1;
0, 0, 1, 0, 0, 1, 0, 0, 1;
1, 1, 0, 1, 1, 0, 1, 1, 0, 1;
1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1;
MATHEMATICA
T[n_, k_]:= If[Abs[JacobiSymbol[Binomial[n, 2], 3] - JacobiSymbol[Binomial[k, 2], 3]]==0, 1, 0];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Oct 20 2021 *)
PROG
(Sage)
def A117904(n, k): return 1 if abs(jacobi_symbol(binomial(n, 2), 3) - jacobi_symbol(binomial(k, 2), 3))==0 else 0
flatten([[A117904(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Oct 20 2021
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Apr 01 2006
STATUS
approved