A346618 - OEIS

%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