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A081009 a(n) = Fibonacci(4n+3) - 1, or Fibonacci(2n+2)*Lucas(2n+1). 1
1, 12, 88, 609, 4180, 28656, 196417, 1346268, 9227464, 63245985, 433494436, 2971215072, 20365011073, 139583862444, 956722026040, 6557470319841, 44945570212852, 308061521170128, 2111485077978049, 14472334024676220, 99194853094755496 (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

Nathaniel Johnston, Table of n, a(n) for n = 0..500

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+[(7/2)-(3/2)*sqrt(5)]^n+[(7/2)+(3/2)*sqrt(5)]^n+(2/5)*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.: (1+4*x)/((1-x)*(1-7*x+x^2)). - Colin Barker, Jun 24 2012

MAPLE

with(combinat) for n from 0 to 30 do printf(`%d, `, fibonacci(4*n+3)-1) od # James A. Sellers, Mar 03 2003

MATHEMATICA

Fibonacci[4*Range[0, 30] +3] -1 (* G. C. Greubel, Jul 14 2019 *)

LinearRecurrence[{8, -8, 1}, {1, 12, 88}, 30] (* Harvey P. Dale, Sep 23 2019 *)

PROG

(MAGMA) [Fibonacci(4*n+3)-1: n in [0..30]]; // Vincenzo Librandi, Apr 15 2011

(PARI) vector(30, n, n--; fibonacci(4*n+3)-1) \\ G. C. Greubel, Jul 14 2019

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

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

CROSSREFS

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

Sequence in context: A057406 A125349 A164608 * A155635 A126507 A181704

Adjacent sequences:  A081006 A081007 A081008 * A081010 A081011 A081012

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 March 8 20:52 EST 2021. Contains 341953 sequences. (Running on oeis4.)