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A131309
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Rabbit-like sequence for phi^2.
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0
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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
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OFFSET
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0,1
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COMMENTS
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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...
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LINKS
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Table of n, a(n) for n=0..32.
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FORMULA
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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.
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EXAMPLE
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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.
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CROSSREFS
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Cf. A027941, A001906.
Sequence in context: A087755 A050072 A156707 * A106510 A163806 A163810
Adjacent sequences: A131306 A131307 A131308 * A131310 A131311 A131312
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson, Jun 27 2007
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STATUS
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approved
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