A081009 a(n) = Fibonacci(4n+3) - 1, or Fibonacci(2n+2)*Lucas(2n+1).

1, 12, 88, 609, 4180, 28656, 196417, 1346268, 9227464, 63245985, 433494436, 2971215072, 20365011073, 139583862444, 956722026040, 6557470319841, 44945570212852, 308061521170128, 2111485077978049, 14472334024676220, 99194853094755496

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).

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