A081072 Fibonacci(4n) + 3, or Fibonacci(2n+2)*Lucas(2n-2).

3, 6, 24, 147, 990, 6768, 46371, 317814, 2178312, 14930355, 102334158, 701408736, 4807526979, 32951280102, 225851433720, 1548008755923, 10610209857726, 72723460248144, 498454011879267, 3416454622906710, 23416728348467688

Offset

0,1

References

Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.

Links

Table of n, a(n) for n=0..20.

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

Formula

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

G.f.: ( -3+18*x ) / ( (x-1)*(x^2-7*x+1) ). a(n) = 3+A033888(n). - R. J. Mathar, Sep 03 2010

a(n) = (A004187(n)+1)*3. - Martin Ettl, Nov 11 2012

Maple

with(combinat): for n from 0 to 40 do printf(`%d, `, fibonacci(4*n)+3) od: # James A. Sellers, Mar 05 2003

Prog

(Magma) [Fibonacci(4*n)+3: n in [0..50]]; // Vincenzo Librandi, Apr 20 2011
(Maxima) makelist(fib(4*n)+3, n, 0, 30); /* Martin Ettl, Nov 11 2012 */
(PARI) Vec((-3+18*x)/((x-1)*(x^2-7*x+1)) + O(x^30)) \\ Michel Marcus, Dec 23 2014

Crossrefs

Cf. A000045 (Fibonacci numbers).

Sequence in context: A109155 A338112 A294381 * A000717 A076020 A018994

Adjacent sequences: A081069 A081070 A081071 * A081073 A081074 A081075

Keyword

nonn,easy

Author

R. K. Guy, Mar 04 2003

Status

approved