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A240910
The sequency numbers of the 32 rows of a Hadamard-Walsh matrix, order 32.
4
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, 13, 18, 5, 26, 10, 21
OFFSET
1,2
COMMENTS
See A240908 for context. This sequence is the natural sequency ordering for an order 32 matrix.
LINKS
Eric Weisstein's World of Mathematics, Hadamard Matrix
Wikipedia, Walsh matrix
FORMULA
Recursion: H(2) = [1 1; 1 -1]; H(n) = H(n-1) * H(2), where * is the Kronecker matrix product.
EXAMPLE
This is a fixed length sequence of only 32 values, as given in full above.
CROSSREFS
Cf. A240908 "natural order" sequencies for Hadamard-Walsh matrix, order 8.
Cf. A240909 "natural order" sequencies for Hadamard-Walsh matrix, order 16.
Cf. A153141 "dyadic order" sequencies for Hadamard-Walsh matrix, all orders.
Cf. A000975(n) is sequency of last row of H(n). - William P. Orrick, Jun 28 2015
Sequence in context: A077397 A040933 A033351 * A297940 A298551 A066434
KEYWORD
nonn,fini,full
AUTHOR
Ross Drewe, Apr 14 2014
EXTENSIONS
Definition of H(n) corrected by William P. Orrick, Jun 28 2015
STATUS
approved