A120529 First differences of successive generalized meta-Fibonacci numbers A120507.

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, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 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^1 ( (1 - z^(3 * [1])) / (1 - z^[1]) + z^4 * (1 - z^(4 * [i]))/(1 - z^[1]) ( (1 - z^(3 * [2])) / (1 - z^[2]) + z^16 * (1 - z^(4 * [2]))/(1 - z^[2]) (..., where [i] = (4^i - 1) / 3.

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

Maple

d := n -> if n=1 then 1 else A120507(n)-A120507(n-1) fi;

Crossrefs

Cf. A120507, A120518.

Sequence in context: A290808 A364252 A190239 * A292301 A099443 A132342

Adjacent sequences: A120526 A120527 A120528 * A120530 A120531 A120532

Keyword

nonn

Author

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

Status

approved