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A081017 a(n) = Lucas(4n+1) - 1, or 5*Fibonacci(2n)*Fibonacci(2n+1). 2
0, 10, 75, 520, 3570, 24475, 167760, 1149850, 7881195, 54018520, 370248450, 2537720635, 17393796000, 119218851370, 817138163595, 5600748293800, 38388099893010, 263115950957275, 1803423556807920, 12360848946698170 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

FORMULA

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

a(n) = -1+(1/2)*(((7/2)-(3/2)*sqrt(5))^n+((7/2)+(3/2)*sqrt(5))^n)+(1/2)*sqrt(5)*(((7/2)+(3/2)*sqrt(5))^n -((7/2)-(3/2)*sqrt(5))^n). - Paolo P. Lava, Dec 01 2008

G.f.: 5*x*(2-x)/((1-x)*(1-7*x+x^2)). - Colin Barker, Apr 16 2012

MAPLE

with(combinat): 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 25 do printf(`%d, `, luc(4*n+1)-1) od: # James A. Sellers, Mar 03 2003

MATHEMATICA

LucasL[4*Range[0, 20]+1]-1 (* or *) LinearRecurrence[{8, -8, 1}, {0, 10, 75}, 20] (* Harvey P. Dale, Mar 02 2015 *)

PROG

(PARI) vector(20, n, n--; f=fibonacci; f(4*n+2)+f(4*n)-1) \\ G. C. Greubel, Jul 14 2019

(MAGMA) [Lucas(4*n+1) -1: n in [0..20]]; // G. C. Greubel, Jul 14 2019

(Sage) [lucas_number2(4*n+1, 1, -1) - 1 for n in (0..20)] # G. C. Greubel, Jul 14 2019

(GAP) List([0..20], n-> Lucas(1, -1, 4*n+1)[2] -1 ); # G. C. Greubel, Jul 14 2019

CROSSREFS

Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers).

Sequence in context: A026935 A110127 A233657 * A238987 A271476 A025015

Adjacent sequences:  A081014 A081015 A081016 * A081018 A081019 A081020

KEYWORD

nonn,easy

AUTHOR

R. K. Guy, Mar 01 2003

EXTENSIONS

More terms from James A. Sellers, Mar 03 2003

STATUS

approved

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Last modified September 22 17:13 EDT 2019. Contains 327311 sequences. (Running on oeis4.)