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

Author

Ross Drewe, Apr 14 2014

Keywords

• nonn
• fini
• full

Comments

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

Examples

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

Links

• N. J. A. Sloane, A Library of Hadamard Matrices
• Eric Weisstein's World of Mathematics, Hadamard Matrix
• Wikipedia, Walsh matrix

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

Formula

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

Extensions

Definition of H(n) corrected by William P. Orrick, Jun 28 2015