

A131309


Rabbitlike sequence for phi^2.


0



1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

Ratio of 1's to 0's tends to phi^2, by way of example, in the subset of 8 terms (1, 1, 0, 1, 1, 0, 1, 0), there are five 1's and three 0's. Subsets have A001906: (1, 3, 8, 21,...); terms; being partial sums of A027941: (1, 4, 12, 33,...). After 33 total terms, there (1 + 3 + 8) zeros and (1 + 2 + 5 + 13) = 21 ones; with the ratio of ones to zeros tending to phi^2 = 2.618...


LINKS

Table of n, a(n) for n=0..32.


FORMULA

Substitution rules T => 2T = t; t => T + t; are derived directly from the matrix generator [2,1; 1,0] (eigenvalue phi^2). Then substitute 1 for T and 0 for t.


EXAMPLE

By rows, we get:
1;
1, 1, 0;
1, 1, 0, 1, 1, 0, 1, 0;
...
Then append nth row to the end of (n1)th row, forming a continuous string.


CROSSREFS

Cf. A027941, A001906.
Sequence in context: A050072 A267576 A156707 * A267208 A106510 A163806
Adjacent sequences: A131306 A131307 A131308 * A131310 A131311 A131312


KEYWORD

nonn


AUTHOR

Gary W. Adamson, Jun 27 2007


STATUS

approved



