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Search: id:A120502
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| A120502 |
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Meta-fibonacci sequence a(n) with parameters s=3. |
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+0
3
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| 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 5, 6, 6, 7, 8, 8, 8, 8, 8, 8, 8, 9, 10, 10, 11, 12, 12, 12, 13, 14, 14, 15, 16, 16, 16, 16, 16, 16, 16, 16, 17, 18, 18, 19, 20, 20, 20, 21, 22, 22, 23, 24, 24, 24
(list; graph; listen)
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OFFSET
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1,5
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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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If 1 <= n <= 4, a(n)=1. If n = 5, then a(n)=2. If n>5 then a(n)=a(n-3-a(n-1)) + a(n-4-a(n-2))
g.f.: A(z) = z * (1 - z^3) / (1 - z) * sum(prod(z^3 * (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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a := proc(n)
option remember;
if n <= 4 then return 1 end if;
if n <= 5 then return 2 end if;
return add(a(n - i - 2 - a(n - i)), i = 1 .. 2)
end proc
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CROSSREFS
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Cf. A120513, A120524.
Sequence in context: A025781 A018119 A143594 this_sequence A099480 A025783 A025780
Adjacent sequences: A120499 A120500 A120501 this_sequence A120503 A120504 A120505
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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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