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

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 16 matrix.

Examples

			This is a fixed length sequence of only 16 values, as given.
		

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. 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).

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

Extensions

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