A120501 - OEIS

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A120501

Meta-Fibonacci sequence a(n) with parameters s=2.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

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 <= 3, a(n)=1. If n = 4, then a(n)=2. If n>4 then a(n)=a(n-2-a(n-1)) + a(n-3-a(n-2)).

G.f.: A(z) = z * (1 - z^2) / (1 - z) * sum(prod(z^2 * (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 <= 3 then return 1 end if;

if n <= 4 then return n-2 end if;

return add(a(n - i - 1 - a(n - i)), i = 1 .. 2)

end proc