|
|
A249450
|
|
Alternate Fibonacci numbers - 2.
|
|
3
|
|
|
-2, -1, 1, 6, 19, 53, 142, 375, 985, 2582, 6763, 17709, 46366, 121391, 317809, 832038, 2178307, 5702885, 14930350, 39088167, 102334153, 267914294, 701408731, 1836311901, 4807526974, 12586269023, 32951280097, 86267571270, 225851433715, 591286729877
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (-2+7*x-3*x^2)/(1-4*x+4*x^2-x^3).
a(n) = 4*a(n-1) - 4*a(n-2) + a(n-3) for n>2.
a(n) = 3*a(n-1) - a(n-2) + 2.
a(n) = (-2-((3-sqrt(5))/2)^n/sqrt(5)+((3+sqrt(5))/2)^n/sqrt(5)). - Colin Barker, Nov 03 2016
|
|
MATHEMATICA
|
Table[Fibonacci[2 n] - 2, {n, 0, 40}] (* or *) CoefficientList[Series[(-2 + 7 x - 3 x^2) / (1 - 4 x + 4 x^2 - x^3), {x, 0, 40}], x]
|
|
PROG
|
(Magma) [Fibonacci(2*n)-2: n in [0..40]];
(PARI) Vec((-2+7*x-3*x^2)/(1-4*x+4*x^2-x^3) + O(x^30)) \\ Colin Barker, Nov 03 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|