A120502 Meta-Fibonacci sequence a(n) with parameters s=3.

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

Offset

1,5

Links

Table of n, a(n) for n=1..60.

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

B. Jackson and F. Ruskey, Meta-Fibonacci Sequences, Binary Trees and Extremal Compact Codes, Electronic Journal of Combinatorics, 13 (2006), #R26, 13 pages.

Formula

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).

Maple

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

Crossrefs

Cf. A120513, A120524.

Sequence in context: A329097 A197054 A337926 * A099480 A025783 A025780

Adjacent sequences: A120499 A120500 A120501 * A120503 A120504 A120505

Keyword

nonn

Author

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

Status

approved