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A081004
a(n) = Fibonacci(4n+2) + 1, or Fibonacci(2n+2)*Lucas(2n).
1
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.
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
KEYWORD
nonn,easy
AUTHOR
R. K. Guy, Mar 01 2003
EXTENSIONS
More terms from James A. Sellers, Mar 03 2003
STATUS
approved