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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
a(n)/3^(3*n) = L(2*n)*L(4*n) = L(2*n) + L(6*n), L=A000032. - Ehren Metcalfe, Apr 21 2018
a(n) = 27^n*F(8*n)/F(2*n), F=A000045. - Ehren Metcalfe, Aug 03 2018
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
Cf. A020876.
Sequence in context: A023099 A209954 A233057 * A134922 A322688 A234233
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Oct 22 2003
STATUS
approved

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)