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A131309 Rabbit-like 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 n-th row to the end of (n-1)-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

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Last modified July 23 22:38 EDT 2019. Contains 325278 sequences. (Running on oeis4.)