A120507 Generalized meta-Fibonacci sequence a(n) with parameters s=0 and k=4.

1, 2, 3, 4, 4, 5, 6, 7, 8, 8, 9, 10, 11, 12, 12, 13, 14, 15, 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, 43, 44, 44, 45, 46, 47

Offset: 1

Author

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

Keywords

• nonn

Links

• 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

Crossrefs

Cf. A120518, A120529.

Programs

Maple

A120507 := proc(n)
    option remember;
    if n <= 4 then return n end if;
    return add(procname(n - i + 1 - procname(n - i)), i = 1 .. 4)
end proc:
seq(A120507(n),n=1..70) ;

Formula

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

G.f.: (z / (1 - z)) * Product_{i>=1} (1 - z^(4 * [i])) / (1 - z^[i]), where [i] = (4^i - 1) / 3.