A081004 a(n) = Fibonacci(4n+2) + 1, or Fibonacci(2n+2)*Lucas(2n).

2, 9, 56, 378, 2585, 17712, 121394, 832041, 5702888, 39088170, 267914297, 1836311904, 12586269026, 86267571273, 591286729880, 4052739537882, 27777890035289, 190392490709136, 1304969544928658, 8944394323791465, 61305790721611592, 420196140727489674

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..600
• Index entries for linear recurrences with constant coefficients, signature (8,-8,1).

Crossrefs

Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers), A056854 (first differences).

Programs

GAP

List([0..30], n-> Fibonacci(4*n+2)+1); # G. C. Greubel, Jul 15 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

Table[Fibonacci[4n+2] +1, {n,0,30}] (* Wesley Ivan Hurt, Nov 20 2014 *)

PARI

vector(30, n, n--; fibonacci(4*n+2)+1) \\ G. C. Greubel, Jul 15 2019

Sage

[fibonacci(4*n+2)+1 for n in (0..30)] # G. C. Greubel, Jul 15 2019

Formula

a(n) = A033890(n)+1.

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

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

Extensions

More terms from James Sellers, Mar 03 2003