login
A240909
The sequency numbers of the 16 rows of a Hadamard-Walsh matrix of order 16.
3
0, 15, 7, 8, 3, 12, 4, 11, 1, 14, 6, 9, 2, 13, 5, 10
OFFSET
1,2
COMMENTS
See A240908 for context. This sequence is the natural sequency ordering for an order 16 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 Kronecker matrix product.
a(n) = A208569(5,n) - 1. - Mathew Englander, Jun 19 2021
EXAMPLE
This is a fixed length sequence of only 16 values, as given.
CROSSREFS
Cf. A240908 "natural order" sequencies for Hadamard-Walsh matrix, order 8.
Cf. A240910 "natural order" sequencies for Hadamard-Walsh matrix, order 32.
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
Cf. A208569 (row 5, minus 1).
Sequence in context: A097532 A033335 A263400 * A133817 A173447 A168211
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