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A120523 First differences of successive meta-Fibonacci numbers A120501. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A075802 A307423 A112526 * A269625 A030315 A119498

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

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Last modified December 8 04:31 EST 2019. Contains 329850 sequences. (Running on oeis4.)