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A081070
Lucas(4n)-2, or 5*Fibonacci(2n)^2.
3
0, 5, 45, 320, 2205, 15125, 103680, 710645, 4870845, 33385280, 228826125, 1568397605, 10749957120, 73681302245, 505019158605, 3461452808000, 23725150497405, 162614600673845, 1114577054219520, 7639424778862805
OFFSET
0,2
REFERENCES
Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
LINKS
Hang Gu and Robert M. Ziff, Crossing on hyperbolic lattices, arXiv:1111.5626 [cond-mat.dis-nn], 2011-2012 (see Eq. 4).
FORMULA
a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3).
a(n) = 5*A049684(n).
G.f.: 5*x*(x+1)/((1-x)*(x^2-7*x+1)). - Colin Barker, Jun 24 2012
MAPLE
luc := proc(n) option remember: if n=0 then RETURN(2) fi: if n=1 then RETURN(1) fi: luc(n-1)+luc(n-2): end: for n from 0 to 40 do printf(`%d, `, luc(4*n)-2) od: # James A. Sellers, Mar 05 2003
MATHEMATICA
LinearRecurrence[{8, -8, 1}, {0, 5, 45}, 20] (* Jean-François Alcover, Nov 24 2017 *)
PROG
(Magma) [Lucas(4*n)-2: n in [0..30]]; // Vincenzo Librandi, Apr 21 2011
(PARI) a(n) = 5*fibonacci(2*n)^2; \\ Michel Marcus, Nov 24 2017
CROSSREFS
Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers), A049684.
Sequence in context: A241275 A343136 A343106 * A247494 A043025 A190540
KEYWORD
nonn,easy
AUTHOR
R. K. Guy, Mar 04 2003
STATUS
approved