nn = 200; t[n_, 1] = If[n == 1, 1, 0];
t[n_, k_] :=
t[n, k] = If[n >= k, Mod[Sum[t[n - i, k - 1], {i, 1, k - 1}], 2], 0];
MatrixPlot[Table[t[n, k], {n, 2*nn}, {k, n}],
ColorFunction -> "Monochrome"] (*Mats Granvik,Dec 06 2019*)
ArrayPlot[CellularAutomaton[30, {{1}, 0}, nn]]