calculus and analysis – Memory issue in Do[] function, computation taking too long. Editing my code


I have the following code:

[Alpha] = 10^4;
[DoubleStruckCapitalT][i_, j_] := Binomial[i, j - 1];
count = 0;
Do[If[[DoubleStruckCapitalT][n, k] != 0 && 
    Mod[[DoubleStruckCapitalT][n, k], 2] == 0, count += 1], {n, 
   0, [Alpha] - 1}, {k, 1, [Alpha]}];
count

This code is taking too long to finish on my PC. Is there a way to edit my code such that is not taking so long?