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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1196

Index entries for linear recurrences with constant coefficients, signature (8,-8,1).

FORMULA

a(n) = 8a(n-1) - 8a(n-2) + a(n-3).

a(n) = -3+(7/2)*{[(7/2)-(3/2)*sqrt(5)]^n+[(7/2)+(3/2)*sqrt(5)]^n}+(3/2)*sqrt(5)*{[(7/2)+(3/2) *sqrt(5)]^n-[(7/2)-(3/2)*sqrt(5)]^n}, with n>=0. - Paolo P. Lava, Dec 01 2008

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: A074751 A129551 A202162 * A220920 A035014 A259989

Adjacent sequences:  A081075 A081076 A081077 * A081079 A081080 A081081

KEYWORD

nonn,easy

AUTHOR

R. K. Guy, Mar 04 2003

STATUS

approved

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Last modified May 18 07:26 EDT 2021. Contains 343995 sequences. (Running on oeis4.)