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

3, 6, 24, 147, 990, 6768, 46371, 317814, 2178312, 14930355, 102334158, 701408736, 4807526979, 32951280102, 225851433720, 1548008755923, 10610209857726, 72723460248144, 498454011879267, 3416454622906710, 23416728348467688, 160500643816367091, 1100087778366101934

Offset: 0

Author

R. K. Guy, Mar 04 2003

Keywords

• nonn
• easy

References

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

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-8,1).

Crossrefs

Cf. A000045 (Fibonacci numbers), A004187, A033888.

Programs

Magma

[Fibonacci(4*n)+3: n in [0..50]]; // Vincenzo Librandi, Apr 20 2011

Maple

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

Mathematica

Fibonacci[4*Range[0, 25]] + 3 (* Paolo Xausa, Jul 03 2025 *)

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

Formula

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

From R. J. Mathar, Sep 03 2010: (Start)

G.f.: ( -3+18*x ) / ( (x-1)*(x^2-7*x+1) ).

a(n) = 3+A033888(n). (End)

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