A120523 First differences of successive meta-Fibonacci numbers A120501.

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

Offset

1,1

Links

Table of n, a(n) for n=1..75.

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

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

G.f.: z (1 + z^3 ( (1 - z^[1]) / (1 - z^[1]) + z^4 * (1 - z^(2 * [i]))/(1 - z^[1]) ( (1 - z^[2]) / (1 - z^[2]) + z^6 * (1 - z^(2 * [2]))/(1 - z^[2]) (..., where [i] = (2^i - 1).

G.f.: D(z) = z * (1 - z^2) * sum(prod(z^2 * (1 - z^(2 * [i])) / (1 - z^[i]), i=1..n), n=0..infinity), where [i] = (2^i - 1).

Maple

d := n -> if n=1 then 1 else A120501(n)-A120501(n-1) fi;

Crossrefs

Cf. A120501, A120512.

Sequence in context: A355684 A355683 A373374 * A269625 A359828 A359781

Adjacent sequences: A120520 A120521 A120522 * A120524 A120525 A120526

Keyword

nonn

Author

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

Status

approved