Table 4.6.2.1

Steurer, W.; Haibach, T.

doi:10.1107/97809553602060000568

International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

pdf | chapter contents | chapter index | related articles

International Tables for Crystallography (2006). Vol. B. ch. 4.6, p. 491 | 1 | 2 |

Table 4.6.2.1

W. Steurer^a ^* and T. Haibach^a

^aLaboratory of Crystallography, Swiss Federal Institute of Technology, CH-8092 Zurich, Switzerland
Correspondence e-mail: w.steurer@kristall.erdw.ethz.ch

Table 4.6.2.1 | top | pdf |
Expansion of the Fibonacci sequence $[B_{n} = \sigma^{n}(\hbox{L})]$ by repeated action of the substitution rule σ: $[\hbox{S} \rightarrow \hbox{L}]$ , $[\hbox{L} \rightarrow \hbox{LS}]$

$[\nu_{\rm L}]$ , $[\nu_{\rm S}]$ are the frequencies of the letters L and S in word $[B_{n}]$ .

$[B_{n}]$	$[\nu_{\rm L}]$	$[\nu_{\rm S}]$	n
L	1	0	0
LS	1	1	1
LSL	2	1	2
LSLLS	3	2	3
LSLLSLSL	5	3	4
LSLLSLSLLSLLS	8	5	5
LSLLSLSLLSLLSLSLLSLSL	13	8	6
	$[\vdots]$	$[\vdots]$	$[\vdots]$
	$[F_{n + 1}]$	$[F_{n}]$	n