A120530 First differences of successive generalized meta-Fibonacci numbers A120508.

1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 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, 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^2 ( (1 - z^(3 * [1])) / (1 - z^[1]) + z^5 * (1 - z^(4 * [i]))/(1 - z^[1]) ( (1 - z^(3 * [2])) / (1 - z^[2]) + z^17 * (1 - z^(4 * [2]))/(1 - z^[2]) (..., where [i] = (4^i - 1) / 3.

G.f.: D(z) = z * (1-z) * Sum_{n>=0} Product_{i=1..n} z * (1 - z^(4 * [i])) / (1 - z^[i]), where [i] = (4^i - 1) / 3.

Maple

d := n -> if n=1 then 1 else A120508(n)-A120508(n-1) fi;

Crossrefs

Cf. A120508, A120519.

Sequence in context: A282339 A175479 A307243 * A078616 A267800 A322980

Adjacent sequences: A120527 A120528 A120529 * A120531 A120532 A120533

Keyword

nonn

Author

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

Status

approved