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

0,1

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).

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

Maple

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

Mathematica

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

Prog

(Magma) [Fibonacci(4*n+2)+1: n in [0..30]]; // Vincenzo Librandi, Apr 15 2011
(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
(GAP) List([0..30], n-> Fibonacci(4*n+2)+1); # G. C. Greubel, Jul 15 2019

Crossrefs

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

Sequence in context: A240562 A091108 A179405 * A198953 A212392 A186262

Adjacent sequences: A081001 A081002 A081003 * A081005 A081006 A081007

Keyword

nonn,easy

Author

R. K. Guy, Mar 01 2003

Extensions

More terms from James A. Sellers, Mar 03 2003

Status

approved