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A120532
First differences of successive generalized meta-Fibonacci numbers A120510.
2
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
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]
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
Sequence in context: A309849 A071906 A104107 * A373156 A320106 A303561
KEYWORD
nonn
AUTHOR
Frank Ruskey and Chris Deugau (deugaucj(AT)uvic.ca), Jun 20 2006
STATUS
approved