A081006 a(n) = Fibonacci(4n) - 1, or Fibonacci(2n+1)*Lucas(2n-1).

2, 20, 143, 986, 6764, 46367, 317810, 2178308, 14930351, 102334154, 701408732, 4807526975, 32951280098, 225851433716, 1548008755919, 10610209857722, 72723460248140, 498454011879263, 3416454622906706, 23416728348467684, 160500643816367087

Offset: 1

Author

R. K. Guy, Mar 01 2003

Keywords

• nonn
• easy

Comments

Apart from the offset, the same as A003481. - R. J. Mathar, Sep 18 2008

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 = 1..500
• Index entries for linear recurrences with constant coefficients, signature (8,-8,1).

Crossrefs

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

Programs

GAP

List([1..30], n-> Fibonacci(4*n)-1); # G. C. Greubel, Jul 15 2019

Magma

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

Maple

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

Mathematica

Fibonacci[4*Range[30]]-1 (* or *) LinearRecurrence[{8,-8,1}, {2,20,143}, 30] (* Harvey P. Dale, Mar 19 2018 *)

PARI

vector(30, n, fibonacci(4*n)-1) \\ G. C. Greubel, Jul 15 2019

Sage

[fibonacci(4*n)-1 for n in (1..30)] # G. C. Greubel, Jul 15 2019

Formula

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

G.f.: x*(2+4*x-x^2)/((1-x)*(1-7*x+x^2)). - Colin Barker, Jun 24 2012

Extensions

More terms from James Sellers, Mar 03 2003