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

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

Crossrefs

Cf. A120507, A120518.

Programs

Maple

d := n -> if n=1 then 1 else A120507(n)-A120507(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^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.