

A120506


Generalized Metafibonacci sequence a(n) with parameters s=3 and k=3.


2



1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 4, 5, 6, 6, 7, 8, 9, 9, 9, 9, 9, 9, 10, 11, 12, 12, 13, 14, 15, 15, 16, 17, 18, 18, 18, 19, 20, 21, 21, 22, 23, 24, 24, 25, 26, 27, 27, 27, 27, 27, 27, 27, 28, 29, 30, 30, 31, 32, 33, 33
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OFFSET

1,5


LINKS

Table of n, a(n) for n=1..60.
C. Deugau and F. Ruskey, Complete kary Trees and Generalized MetaFibonacci Sequences, J. Integer Seq., Vol. 12. [This is a later version than that in the GenMetaFib.html link]
C. Deugau and F. Ruskey, Complete kary Trees and Generalized MetaFibonacci Sequences


FORMULA

If 1 <= n <= 4, a(n)=1. If 5 <= n <= 6, then a(n)=n3. If n>6 then a(n)=a(n3a(n1)) + a(n4a(n2)) + a(n5a(n3))
g.f.: A(z) = z * (1  z^3) / (1  z) * sum(prod(z^3 * (1  z^(3 * [i])) / (1  z^[i]), i=1..n), n=0..infinity), where [i] = (3^i  1) / 2.


MAPLE

a := proc(n)
option remember;
if n <= 4 then return 1 end if;
if n <= 6 then return n3 end if;
return add(a(n  i  2  a(n  i)), i = 1 .. 3)
end proc


CROSSREFS

Cf. A120517, A120528.
Sequence in context: A080344 A194225 A025782 * A327041 A277267 A246262
Adjacent sequences: A120503 A120504 A120505 * A120507 A120508 A120509


KEYWORD

nonn


AUTHOR

Frank Ruskey and Chris Deugau (deugaucj(AT)uvic.ca), Jun 20 2006


STATUS

approved



