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%I #22 Aug 21 2021 01:00:00
%S 0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,
%T 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,1,0,0,1,0,1,0,0,1,0,0,0,
%U 0,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0
%N Triangle read by rows: T(n,k) = 1 iff 2 divides binomial(n,k) but 4 does not (0 <= k <= n).
%H P. Goetgheluck, <a href="https://www.jstor.org/stable/2323099">Computing binomial coefficients</a>, The American Mathematical Monthly 94.4 (1987): 360-365. See Fig. 2.
%e Triangle begins:
%e 0,
%e 0, 0,
%e 0, 1, 0,
%e 0, 0, 0, 0,
%e 0, 0, 1, 0, 0,
%e 0, 0, 1, 1, 0, 0,
%e 0, 1, 0, 0, 0, 1, 0,
%e 0, 0, 0, 0, 0, 0, 0, 0,
%e 0, 0, 0, 0, 1, 0, 0, 0, 0,
%e 0, 0, 0, 0, 1, 1, 0, 0, 0, 0,
%e 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0,
%e 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0,
%e 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
%e ...
%Y Cf. A007318, A007814, A047999, A346619.
%K nonn,tabl
%O 0
%A _N. J. A. Sloane_, Aug 21 2021