Abstract
It is shown that for 1 ⩽ j ⩽ n and 1 ⩽ k ⩽ 2″, the jth letter of the kth word of the binary reflected Gray code of length n is equal to the parity of the binomial coefficient 2 n−2 n−j−1 C [2 n−2 n−j−1−k/2] modulo 2. Also it is shown how this observation and the usual iterative definition of the binary reflected Gray codes are revealed in a modified version of Sierpinski's gasket (Pascal's triangle modulo 2).
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