|
|
A025169
|
|
a(n) = 2*Fibonacci(2*n+2).
|
|
14
|
|
|
2, 6, 16, 42, 110, 288, 754, 1974, 5168, 13530, 35422, 92736, 242786, 635622, 1664080, 4356618, 11405774, 29860704, 78176338, 204668310, 535828592, 1402817466, 3672623806, 9615053952, 25172538050, 65902560198, 172535142544
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
The pairs (x, y) = (a(n), a(n+1)) satisfy x^2 + y^2 = 3*x*y + 4. - Michel Lagneau, Feb 01 2014
|
|
LINKS
|
|
|
FORMULA
|
G.f.: 2/(1 - 3*x + x^2).
a(n) = 3*a(n-1) - a(n-2).
|
|
MAPLE
|
|
|
MATHEMATICA
|
Table[2Fibonacci[2n+2], {n, 0, 30}] (* or *)
CoefficientList[Series[2/(1-3x+x^2), {x, 0, 30}], x] (* Michael De Vlieger, Mar 09 2016 *)
|
|
PROG
|
(PARI) a(n)=2*fibonacci(2*n+2)
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 2/(1-3*x + x^2) )); // Marius A. Burtea, Jan 16 2020
(Haskell)
a025169 n = a025169_list !! n
a025169_list = 2 : 6 : zipWith (-) (map (* 3) $ tail a025169_list) a025169_list
(Sage) [2*fibonacci(2*n+2) for n in (0..30)] # G. C. Greubel, Jan 16 2020
(GAP) List([0..30], n-> 2*Fibonacci(2*n+2) ); # G. C. Greubel, Jan 16 2020
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|