|
|
A088210
|
|
Numerators of convergents of the continued fraction with the n+1 partial quotients: [2;2,2,...(n 2's)...,2,n+1], starting with [1], [2;2], [2;2,3], [2;2,2,4], ...
|
|
3
|
|
|
1, 5, 17, 53, 157, 449, 1253, 3433, 9273, 24765, 65529, 172061, 448853, 1164409, 3006157, 7728337, 19794545, 50532469, 128621281, 326513669, 826887693, 2089505841, 5269572021, 13265211961, 33336792745, 83648953133, 209591807177
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
|
|
REFERENCES
|
R. P. Grimaldi, Ternary strings with no consecutive 0's and no consecutive 1's, Congressus Numerantium, 205 (2011), 129-149. (See the foot of page 136.)
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1+x)(1-x^2)/(1-2*x-x^2)^2.
|
|
EXAMPLE
|
a(3)/A088211(3) = [2;2,2,4] = 53/22.
|
|
MATHEMATICA
|
LinearRecurrence[{4, -2, -4, -1}, {1, 5, 17, 53}, 30] (* Paolo Xausa, Feb 08 2024 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
frac,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|