A120526 First differences of successive generalized meta-Fibonacci numbers A120504.

1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1

Offset

1,1

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

d(n) = 0 if node n is an inner node, or 1 if node n is a leaf.

G.f.: z (1 + z^2 ( (1 - z^(2 * [1])) / (1 - z^[1]) + z^4 * (1 - z^(3 * [i]))/(1 - z^[1]) ( (1 - z^(2 * [2])) / (1 - z^[2]) + z^10 * (1 - z^(3 * [2]))/(1 - z^[2]) (..., where [i] = (3^i - 1) / 2.

G.f.: D(z) = (1 - 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

d := n -> if n=1 then 1 else A120504(n)-A120504(n-1) fi;

Mathematica

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

Crossrefs

Cf. A120504, A120515.

Sequence in context: A118175 A179762 A263804 * A086694 A357518 A093317

Adjacent sequences: A120523 A120524 A120525 * A120527 A120528 A120529

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