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Search: id:A120509
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| A120509 |
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Generalized Meta-fibonacci sequence a(n) with parameters s=2 and k=4. |
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+0
3
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| 1, 1, 1, 2, 3, 4, 4, 4, 4, 5, 6, 7, 8, 8, 9, 10, 11, 12, 12, 13, 14, 15, 16, 16, 16, 16, 16, 17, 18, 19, 20, 20, 21, 22, 23, 24, 24, 25, 26, 27, 28, 28, 29, 30, 31, 32, 32, 32, 33, 34, 35, 36, 36, 37, 38, 39, 40, 40, 41, 42
(list; graph; listen)
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OFFSET
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1,4
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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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g.f.: A(z) = z * (1 - z^2) / (1 - z) * sum(prod(z^2 * (1 - z^(4 * [i])) / (1 - z^[i]), i=1..n), n=0..infinity), where [i] = (4^i - 1) / 3.
If 1 <= n <= 3, a(n)=1. If 4 <= n <= 6, then a(n)=n-2. If n>6 then a(n)=a(n-2-a(n-1)) + a(n-3-a(n-2)) + a(n-4-a(n-3)) + a(n-5-a(n-4))
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MAPLE
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a := proc(n)
option remember;
if n <= 3 then return 1 end if;
if n <= 6 then return n-2 end if;
return add(a(n - i - 1 - a(n - i)), i = 1 .. 4)
end proc
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CROSSREFS
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Cf. A120520, A120531.
Sequence in context: A087844 A140427 A072229 this_sequence A029106 A064004 A087827
Adjacent sequences: A120506 A120507 A120508 this_sequence A120510 A120511 A120512
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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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