|
|
A051958
|
|
a(n) = 2 a(n-1) + 24 a(n-2), a(0)=0, a(1)=1.
|
|
9
|
|
|
0, 1, 2, 28, 104, 880, 4256, 29632, 161408, 1033984, 5941760, 36699136, 216000512, 1312780288, 7809572864, 47125872640, 281681494016, 1694383931392, 10149123719168, 60963461791744, 365505892843520, 2194134868688896
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
The ratio a(n+1)/a(n) converges to 6 as n approaches infinity. - Felix P. Muga II, Mar 10 2014
|
|
REFERENCES
|
F. P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, March 2014; Preprint on ResearchGate.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x/((1+4*x)*(1-6*x)).
a(n) = (6^n - (-4)^n)/10.
|
|
MATHEMATICA
|
CoefficientList[Series[x / ((1 + 4 x) (1 - 6 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Mar 08 2014 *)
LinearRecurrence[{2, 24}, {0, 1}, 30] (* Harvey P. Dale, May 08 2022 *)
|
|
PROG
|
(PARI) a(n)=(6^n-(-4)^n)/10
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|