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%I #27 Dec 16 2017 23:25:00
%S 1,2,2,4,3,8,8,8,12,12,16,12,5,4,192,32,32,10,10,64,64,64,48,128,15,
%T 160,128,240,128,128,192,192,240,240,80,80,256,192,80,64,17,80,96,160,
%U 20480,512,512,160,160,34,34,176,176,40960,40960,1024
%N Compressed nim-multiplication table read by antidiagonals.
%C A nim-multiplication table (A051775) of size 2^2^n can be compressed to a matrix of size 2^n, using Walsh permutations. As the nim-multiplication tables are submatrices to the bigger ones, also the compressions are submatrices to the bigger ones, leading to this infinite array.
%C This array is closely related to the nim-multiplication table powers of 2 (A223541). Both arrays can be seen as different views of the same cubic binary tensor.
%C The diagonal is A001317 (Sierpinski triangle rows read like binary numbers).
%C The elements of this array are listed in A223539. In the key-matrix A223538 the entries of this array (which become very large) are replaced by the corresponding index numbers of A223539. (Surprisingly, the key-matrix seems to be interesting on its own.)
%H Tilman Piesk, <a href="/A223537/b223537.txt">First 128 rows of the matrix, flattened</a>
%H Tilman Piesk, <a href="http://commons.wikimedia.org/wiki/Category:Compressed_nim-multiplication_table;_dual">Elements of dual matrix</a> (256 SVGs)
%H Tilman Piesk, <a href="http://en.wikiversity.org/wiki/Walsh_permutation;_nimber_multiplication">Walsh permutation; nimber multiplication</a> (Wikiversity)
%H Tilman Piesk, <a href="http://pastebin.com/uqD9x7hW">MATLAB functions cv2cm and cm2cv</a>
%F a(m,n) = A223539( A223538(m,n) ).
%F a(n,n) = A001317(n).
%F a(1,n) = A134683(n+1).
%o ( Calculation of this matrix B from matrix A = A223541 with MATLAB: )
%o B = bin([256 256],'pre') ;
%o for m=1:256
%o B(m,1:256) = cm2cv( cv2cm( A(m,1:256) )' ) ;
%o end
%o ( The functions are linked above. See also the MATLAB code for A223541. )
%Y Cf. A051775, A223541, A001317, A223539, A223538.
%K nonn,tabl
%O 0,2
%A _Tilman Piesk_, Mar 21 2013
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