A120532 First differences of successive generalized meta-Fibonacci numbers A120510.

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

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^4 ( (1 - z^(3 * [1])) / (1 - z^[1]) + z^7 * (1 - z^(4 * [i]))/(1 - z^[1]) ( (1 - z^(3 * [2])) / (1 - z^[2]) + z^19 * (1 - z^(4 * [2]))/(1 - z^[2]) (..., where [i] = (4^i - 1) / 3.

g.f.: D(z) = z * (1 - z^3) * sum(prod(z^3 * (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 A120510(n)-A120510(n-1) fi;

Crossrefs

Cf. A120510, A120521.

Sequence in context: A309849 A071906 A104107 * A373156 A320106 A303561

Adjacent sequences: A120529 A120530 A120531 * A120533 A120534 A120535

Keyword

nonn

Author

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

Status

approved