login
A305573
Number of (1,1) pairs occurring at depth 3n of the Fibonacci tree.
0
1, 5, 27, 152, 879, 5181, 30980, 187352, 1143447, 7031999, 43524851, 270892380, 1694120644, 10639643324, 67071402168, 424231073712, 2691390885735, 17121286350819, 109187993381489, 697911059909408
OFFSET
0,2
REFERENCES
John Charles Saunders, Problems in Combinatorial and Analytic Number Theory, Ph. D. thesis, University of Waterloo, 2018.
LINKS
Kevin G. Hare, and J. C. Saunders, On (a,b) Pairs in Random Fibonacci Sequences, Arxiv preprint, arXiv:1608.03522 [math.NT], February 2018.
FORMULA
From Vladimir Kruchinin, Sep 30 2023: (Start)
G.f.: (F(x) - 1)/(2 - F(x))^2/x, where F(x) is the g.f. of A001764.
a(n) = 3*Sum_{k=0..n} (k + 1)^2*C(3*n + 2, n - k)/(2*n + k + 3). (End)
CROSSREFS
Sequence in context: A162557 A134425 A332598 * A184702 A083326 A083880
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Jun 05 2018
STATUS
approved