OFFSET
0,5
COMMENTS
For the complex Lucas function L(z) and its zeros see the comments in A214671 and the Koshy reference.
REFERENCES
Thomas Koshy, "Fibonacci and Lucas Numbers with Applications", John Wiley and Sons, 2001.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = floor((2*n+1)*b/2), n >= 0, with b/2 = -y_0(0) = 2*Pi*log(phi) / (Pi^2 + (2*log(phi))^2), with phi = (1+sqrt(5))/2. Note that b/2 is approximately 0.2800649542... . The constant b appears in the corresponding Fibonacci case A214656.
MATHEMATICA
Table[Floor[(2*n+1)*(2*Pi*Log[GoldenRatio])/(Pi^2 + (2*Log[GoldenRatio])^2)], {n, 0, 100}] (* G. C. Greubel, Mar 09 2024 *)
PROG
(Magma) R:= RealField(100); [Floor((2*n+1)*(2*Pi(R)*Log((1 + Sqrt(5))/2))/(Pi(R)^2 + (2*Log((1+Sqrt(5))/2))^2)) : n in [0..100]]; // G. C. Greubel, Mar 09 2024
(SageMath) [floor(2*(2*n+1)*pi*log(golden_ratio)/(pi^2 +4*(log(golden_ratio))^2)) for n in range(101)] # G. C. Greubel, Mar 09 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Wolfdieter Lang, Jul 25 2012
STATUS
approved