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A081078
a(n) = Lucas(4n) - 3, or Lucas(2n-1)*Lucas(2n+1).
1
4, 44, 319, 2204, 15124, 103679, 710644, 4870844, 33385279, 228826124, 1568397604, 10749957119, 73681302244, 505019158604, 3461452807999, 23725150497404, 162614600673844, 1114577054219519, 7639424778862804, 52361396397820124, 358890350005878079
OFFSET
1,1
REFERENCES
Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
FORMULA
a(n) = 8a(n-1) - 8a(n-2) + a(n-3).
From R. J. Mathar, Sep 03 2010: (Start)
G.f.: x*(-4-12*x+x^2) / ( (x-1)*(x^2-7*x+1)).
a(n) = A056854(n)-3. (End)
From Peter Bala, Nov 30 2013: (Start)
a(n) = Lucas(2*n)^2 - 5.
Sum_{n>=1} 1/a(n) = (5 - sqrt(5))/10. (End)
Sum_{n>=1} 1/a(n) = A244847. - Amiram Eldar, Oct 27 2020
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 1 to 40 do printf(`%d, `, luc(4*n)-3) od: # James A. Sellers, Mar 05 2003
MATHEMATICA
LinearRecurrence[{8, -8, 1}, {4, 44, 319}, 30] (* Harvey P. Dale, Jun 08 2014 *)
Table[LucasL[4*n] - 3, {n, 1, 20}] (* Amiram Eldar, Oct 27 2020 *)
PROG
(PARI) Vec(x*(-4-12*x+x^2) / ( (x-1)*(x^2-7*x+1)) + O(x^30)) \\ Michel Marcus, Dec 23 2014
CROSSREFS
Cf. A000032 (Lucas numbers), A056854 (Lucas(4n)), A244847.
Sequence in context: A129551 A202162 A354646 * A220920 A035014 A259989
KEYWORD
nonn,easy
AUTHOR
R. K. Guy, Mar 04 2003
STATUS
approved