A120531 First differences of successive generalized meta-Fibonacci numbers A120509.

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

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

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^(3 * [1])) / (1 - z^[1]) + z^6 * (1 - z^(4 * [i]))/(1 - z^[1]) ( (1 - z^(3 * [2])) / (1 - z^[2]) + z^18 * (1 - z^(4 * [2]))/(1 - z^[2]) (..., where [i] = (4^i - 1) / 3.

g.f.: D(z) = z * (1 - z^2) * sum(prod(z^2 * (1 - z^(4 * [i])) / (1 - z^[i]), i=1..n), n=0..infinity), where [i] = (4^i - 1) / 3.

Maple

d := n -> if n=1 then 1 else A120509(n)-A120509(n-1) fi;

Crossrefs

Cf. A120509, A120520.

Sequence in context: A364746 A051341 A057211 * A106665 A004609 A287674

Adjacent sequences: A120528 A120529 A120530 * A120532 A120533 A120534

Keyword

nonn

Author

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

Status

approved