A240909 The sequency numbers of the 16 rows of a Hadamard-Walsh matrix of order 16.

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

Table of n, a(n) for n=1..16.

N. J. A. Sloane, A Library of Hadamard Matrices

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) = A131271(4,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. A131271 (row 4, minus 1).

Sequence in context: A097532 A033335 A263400 * A133817 A173447 A377612

Adjacent sequences: A240906 A240907 A240908 * A240910 A240911 A240912

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