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A081069
Lucas(4n)+2, or Lucas(2n)^2.
3
4, 9, 49, 324, 2209, 15129, 103684, 710649, 4870849, 33385284, 228826129, 1568397609, 10749957124, 73681302249, 505019158609, 3461452808004, 23725150497409, 162614600673849, 1114577054219524, 7639424778862809
OFFSET
0,1
REFERENCES
Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
FORMULA
a(n) = A005248(n)^2 = A056854(n)+2.
a(n) = 8a(n-1) - 8a(n-2) + a(n-3).
a(n) = 2^(4*n)*(cos(Pi/5)^(2*n)+cos(3*Pi/5)^(2*n))^2. - Gary Detlefs, Dec 05 2010
a(n) = 7*a(n-1)-a(n-2)-10, n>1. - Gary Detlefs, Dec 06 2010
a(n) = 5*sum(fibonacci(4*k+2),k=0..n)+4, with offset -1. - Gary Detlefs, Dec 06 2010
G.f.: -(9*x^2-23*x+4)/((x-1)*(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
G:=(x, n)-> cos(x)^n +cos(3*x)^n: seq(simplify(2^(4*n)*G(Pi/5, 2*n)^2), n=0..19) # Gary Detlefs, Dec 05 2010
t:= n-> sum(fibonacci(4*k+2), k=0..n):seq(5*t(n)+4, n=-1..18); # Gary Detlefs, Dec 06 2010
MATHEMATICA
LucasL[4*Range[0, 20]]+2 (* Harvey P. Dale, Sep 09 2012 *)
PROG
(Magma) [ Lucas(2*n)^2: n in [0..70] ]; // Vincenzo Librandi, Apr 16 2011
CROSSREFS
Cf. A000032 (Lucas numbers).
Sequence in context: A231177 A110481 A030088 * A053967 A028945 A086541
KEYWORD
nonn,easy
AUTHOR
R. K. Guy, Mar 04 2003
STATUS
approved