A240910 The sequency numbers of the 32 rows of a Hadamard-Walsh matrix, order 32.

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

Table of n, a(n) for n=1..32.

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 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

Adjacent sequences: A240907 A240908 A240909 * A240911 A240912 A240913

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