OFFSET
0
COMMENTS
The binary Walsh matrix of order 2^n, using natural ordering, is the 2^n-th principal submatrix of this matrix.
This sequence begins to diverge from A219463 at n=24, corresponding to (i,j)=(3,3).
LINKS
Eric Weisstein's World of Mathematics, Walsh Function
Wikipedia, Walsh matrix
EXAMPLE
Top left corner of infinite binary Walsh matrix:
0 0 0 0 0 0 0 0
0 1 0 1 0 1 0 1
0 0 1 1 0 0 1 1
0 1 1 0 0 1 1 0
0 0 0 0 1 1 1 1
0 1 0 1 1 0 1 0
0 0 1 1 1 1 0 0
0 1 1 0 1 0 0 1
MATHEMATICA
Flatten[Table[
Mod[DigitCount[BitAnd[k, n - k], 2, 1], 2], {n, 0, 14}, {k, 0, n}]]
PROG
(PARI) A(i, j) = hammingweight(bitand(i, j)) % 2
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Jeremy Tan, Dec 23 2021
STATUS
approved