A120522 First differences of successive meta-Fibonacci numbers A006949.

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

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
• B. Jackson and F. Ruskey, Meta-Fibonacci Sequences, Binary Trees and Extremal Compact Codes, Electronic Journal of Combinatorics, 13 (2006), #R26, 13 pages.

Crossrefs

Cf. A006949, A120511.

Programs

Maple

d := n -> if n=1 then 1 else A006949(n)-A006949(n-1) fi;

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^[1]) / (1 - z^[1]) + z^3 * (1 - z^(2 * [i]))/(1 - z^[1]) ( (1 - z^[2]) / (1 - z^[2]) + z^5 * (1 - z^(2 * [2]))/(1 - z^[2]) (..., where [i] = (2^i - 1).