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%I #7 Jan 20 2022 08:48:43
%S 0,0,0,0,1,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,
%T 0,0,0,1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0,0,0,
%U 0,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,1,0,0
%N Infinite binary Walsh matrix read by antidiagonals.
%C The binary Walsh matrix of order 2^n, using natural ordering, is the 2^n-th principal submatrix of this matrix.
%C This sequence begins to diverge from A219463 at n=24, corresponding to (i,j)=(3,3).
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WalshFunction.html">Walsh Function</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Walsh_matrix">Walsh matrix</a>
%F A(i,j) = A010060(A004198(i,j)) = hammingweight(i AND j) mod 2.
%e Top left corner of infinite binary Walsh matrix:
%e 0 0 0 0 0 0 0 0
%e 0 1 0 1 0 1 0 1
%e 0 0 1 1 0 0 1 1
%e 0 1 1 0 0 1 1 0
%e 0 0 0 0 1 1 1 1
%e 0 1 0 1 1 0 1 0
%e 0 0 1 1 1 1 0 0
%e 0 1 1 0 1 0 0 1
%t Flatten[Table[
%t Mod[DigitCount[BitAnd[k, n - k], 2, 1], 2], {n, 0, 14}, {k, 0, n}]]
%o (PARI) A(i,j) = hammingweight(bitand(i,j)) % 2
%Y Cf. A197818 (negated antidiagonals as decimal), A228539, A228540.
%K nonn,tabl
%O 0
%A _Jeremy Tan_, Dec 23 2021
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