Here's another suggestion, using the binomial coefficients mod 2. In J504:
v=:13 : '2 | (i.>:y.)!y.'
line=:13 : '((x.-y.)#'' ''),(": v y.)'"0
triangle=:13 : 'y. line i.y.'
triangle 10
1
1 1
1 0 1
1 1 1 1
1 0 0 0 1
1 1 0 0 1 1
1 0 1 0 1 0 1
1 1 1 1 1 1 1 1
1 0 0 0 0 0 0 0 1
1 1 0 0 0 0 0 0 1 1
Best wishes,
John
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