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Search: id:A120523
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| A120523 |
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First differences of successive meta-Fibonacci numbers A120501. |
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+0
3
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| 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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B. Jackson and F. Ruskey, Meta-Fibonacci Sequences, Binary Trees and Extremal Compact Codes, Electronic Journal of Combinatorics, 13 (2006), #R26, 13 pages.
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LINKS
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C. Deugau and F. Ruskey, Complete k-ary Trees and Generalized Meta-Fibonacci Sequences, J. Integer Seq., Vol. 12. [This is a later version than that in the GenMetaFib.html link]
C. Deugau and F. Ruskey, Complete k-ary Trees and Generalized Meta-Fibonacci Sequences
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FORMULA
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d(n) = 0 if node n is an inner node, or 1 if node n is a leaf.
g.f.: z (1 + z^3 ( (1 - z^[1]) / (1 - z^[1]) + z^4 * (1 - z^(2 * [i]))/(1 - z^[1]) ( (1 - z^[2]) / (1 - z^[2]) + z^6 * (1 - z^(2 * [2]))/(1 - z^[2]) (..., where [i] = (2^i - 1).
g.f.: D(z) = z * (1 - z^2) * sum(prod(z^2 * (1 - z^(2 * [i])) / (1 - z^[i]), i=1..n), n=0..infinity), where [i] = (2^i - 1).
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MAPLE
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d := n -> if n=1 then 1 else A120501(n)-A120501(n-1) fi;
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CROSSREFS
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Cf. A120501, A120512.
Sequence in context: A065803 A075802 A112526 this_sequence A119498 A070912 A014108
Adjacent sequences: A120520 A120521 A120522 this_sequence A120524 A120525 A120526
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KEYWORD
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nonn
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AUTHOR
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Frank Ruskey (http://www.cs.uvic.ca/~ruskey/) and Chris Deugau (deugaucj(AT)uvic.ca), Jun 20 2006
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