A120504 Generalized meta-Fibonacci sequence a(n) with parameters s=1 and k=3.

1, 1, 2, 3, 3, 3, 4, 5, 6, 6, 7, 8, 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, 28, 29, 30, 30, 31, 32, 33, 33, 34, 35, 36, 36, 36, 37, 38, 39, 39, 40, 41, 42, 42, 43, 44, 45, 45, 45, 46, 47, 48, 48, 49

Offset

1,3

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

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.

Formula

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

G.f.: A(z) = z * sum(prod(z * (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 <= 2 then return 1 end if;
if n <= 4 then return n-1 end if;
return add(a(n - i - a(n - i)), i = 1 .. 3)
end proc;

Mathematica

A120504[n_] := A120504[n] = Which[n <= 2, 1, n <= 4, n-1, True, Sum[A120504[n-i-A120504[n-i]], {i, 3}]];
Array[A120504, 100] (* Paolo Xausa, Mar 26 2026 *)

Crossrefs

Cf. A120515, A120526.

Sequence in context: A379067 A072688 A381018 * A025772 A211535 A029069

Adjacent sequences: A120501 A120502 A120503 * A120505 A120506 A120507

Keyword

nonn

Author

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

Extensions

More terms from Paolo Xausa, Mar 26 2026

Status

approved