A081008 a(n) = Fibonacci(4n+2) - 1, or Fibonacci(2n)*Lucas(2n+2).

0, 7, 54, 376, 2583, 17710, 121392, 832039, 5702886, 39088168, 267914295, 1836311902, 12586269024, 86267571271, 591286729878, 4052739537880, 27777890035287, 190392490709134, 1304969544928656, 8944394323791463, 61305790721611590, 420196140727489672

Offset: 0

Author

R. K. Guy, Mar 01 2003

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

GAP

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

Magma

[Fibonacci(4*n+2)-1: n in [0..30]]; // Vincenzo Librandi, Apr 15 2011

Maple

with(combinat) for n from 0 to 30 do printf(`%d,`,fibonacci(4*n+2)-1) od # James Sellers, Mar 03 2003

Mathematica

Fibonacci[4Range[25]-2]-1 (* or *)
LinearRecurrence[{8,-8,1},{0,7,54},25] (* Paolo Xausa, Jan 08 2024 *)

PARI

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

Sage

[fibonacci(4*n+2)-1 for n in (0..30)] # G. C. Greubel, Jul 14 2019

Formula

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

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

Extensions

More terms from James Sellers, Mar 03 2003