|
|
A087424
|
|
a(n) = S(4*n,4)/S(n,4) where S(n,m) = Sum_{k=0..n} binomial(n,k)*Fibonacci(m*k).
|
|
2
|
|
|
567, 239841, 114082668, 55125843489, 26697877691247, 12934267027240356, 6266540498895923463, 3036106030479071781249, 1470978970343729016987852, 712682440446248640284336721, 345291321126117622870522555983, 167292036479044881831300837903684, 81052212349412217472309893818152407
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
a(n) = (243+108*sqrt(5))^n+(243-108*sqrt(5))^n+((81+27*sqrt(5))/2)^n+((81-27*sqrt(5))/2)^n.
G.f.: -81*x*(26244*x^3-15309*x^2+1008*x-7) / ((729*x^2-486*x+1)*(729*x^2-81*x+1)). - Colin Barker, Dec 01 2012
|
|
MATHEMATICA
|
Table[(27^n Fibonacci[8 n] / Fibonacci[2 n]), {n, 15}] (* Vincenzo Librandi, Aug 04 2018 *)
LinearRecurrence[{567, -40824, 413343, -531441}, {567, 239841, 114082668, 55125843489}, 20] (* Harvey P. Dale, Jun 23 2020 *)
|
|
PROG
|
(Magma) [27^n*Fibonacci(8*n)/Fibonacci(2*n): n in [1..15]]; // Vincenzo Librandi, Aug 04 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|