login
A081010
a(n) = Fibonacci(4n+1) + 2, or Fibonacci(2n-1)*Lucas(2n+2).
1
3, 7, 36, 235, 1599, 10948, 75027, 514231, 3524580, 24157819, 165580143, 1134903172, 7778742051, 53316291175, 365435296164, 2504730781963, 17167680177567, 117669030460996, 806515533049395, 5527939700884759, 37889062373143908, 259695496911122587
OFFSET
0,1
REFERENCES
Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
FORMULA
a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3).
a(n) = 2 + (A001906(n+1)^2 + A001519(n)^2)/2. - Creighton Dement, Aug 15 2004
G.f.: (3-17*x+4*x^2)/((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+1)+2) od # James A. Sellers, Mar 03 2003
MATHEMATICA
Fibonacci[4*Range[0, 30]+1]+2 (* G. C. Greubel, Jul 14 2019 *)
PROG
(Magma) [Fibonacci(4*n+1) +2: n in [0..30]]; // Vincenzo Librandi, Apr 15 2011
(PARI) vector(30, n, n--; fibonacci(4*n+1)+2) \\ G. C. Greubel, Jul 14 2019
(Sage) [fibonacci(4*n+1)+2 for n in (0..30)] # G. C. Greubel, Jul 14 2019
(GAP) List([0..30], n-> Fibonacci(4*n+1)+2); # G. C. Greubel, Jul 14 2019
CROSSREFS
Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers).
Sequence in context: A102917 A156465 A049366 * A100377 A270396 A167169
KEYWORD
nonn,easy
AUTHOR
R. K. Guy, Mar 01 2003
EXTENSIONS
More terms from James A. Sellers, Mar 03 2003
STATUS
approved