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The sequency numbers of the 32 rows of a Hadamard-Walsh matrix, order 32.
5

%I #20 Jun 29 2015 01:40:49

%S 0,31,15,16,7,24,8,23,3,28,12,19,4,27,11,20,1,30,14,17,6,25,9,22,2,29,

%T 13,18,5,26,10,21

%N The sequency numbers of the 32 rows of a Hadamard-Walsh matrix, order 32.

%C See A240908 for context. This sequence is the natural sequency ordering for an order 32 matrix.

%H N. J. A. Sloane, <a href="http://neilsloane.com/hadamard">A Library of Hadamard Matrices</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HadamardMatrix.html">Hadamard Matrix</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Walsh_matrix">Walsh matrix</a>

%F Recursion: H(2) = [1 1; 1 -1]; H(n) = H(n-1) * H(2), where * is the Kronecker matrix product.

%e This is a fixed length sequence of only 32 values, as given in full above.

%Y Cf. A240908 "natural order" sequencies for Hadamard-Walsh matrix, order 8.

%Y Cf. A240909 "natural order" sequencies for Hadamard-Walsh matrix, order 16.

%Y Cf. A153141 "dyadic order" sequencies for Hadamard-Walsh matrix, all orders.

%Y Cf. A000975(n) is sequency of last row of H(n). - _William P. Orrick_, Jun 28 2015

%K nonn,fini,full

%O 1,2

%A _Ross Drewe_, Apr 14 2014

%E Definition of H(n) corrected by _William P. Orrick_, Jun 28 2015