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A081015 a(n) = Lucas(4n+3) + 1, or 5*Fibonacci(2n+1)*Fibonacci(2n+2). 2
5, 30, 200, 1365, 9350, 64080, 439205, 3010350, 20633240, 141422325, 969323030, 6643838880, 45537549125, 312119004990, 2139295485800, 14662949395605, 100501350283430, 688846502588400, 4721424167835365, 32361122672259150 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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+2*{[(7/2)-(3/2)*sqrt(5)]^n+[(7/2)+(3/2)*sqrt(5)]^n}+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

G.f.: 5*(1-2*x)/((1-x)*(1-7*x+x^2)). - 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 25 do printf(`%d, `, luc(4*n+3)+1) od: # James A. Sellers, Mar 03 2003

MATHEMATICA

LucasL[4*Range[0, 20] +3] +1 (* G. C. Greubel, Jul 14 2019 *)

PROG

(PARI) vector(30, n, n--; f=fibonacci; f(4*n+4)+f(4*n+2)+1) \\ G. C. Greubel, Jul 14 2019

(MAGMA) [Lucas(4*n+3)+1: n in [0..30]]; // G. C. Greubel, Jul 14 2019

(Sage) [lucas_number2(4*n+3, 1, -1)+1 for n in (0..30)] # G. C. Greubel, Jul 14 2019

(GAP) List([0..30], n-> Lucas(1, -1, 4*n+3)[2] +1); # G. C. Greubel, Jul 14 2019

CROSSREFS

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

Sequence in context: A034164 A322257 A103433 * A090139 A107265 A196678

Adjacent sequences:  A081012 A081013 A081014 * A081016 A081017 A081018

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 15 14:28 EDT 2019. Contains 327078 sequences. (Running on oeis4.)