A081074 Fibonacci(4n)-3, or Fibonacci(2n-2)*Lucas(2n+2).

0, 18, 141, 984, 6762, 46365, 317808, 2178306, 14930349, 102334152, 701408730, 4807526973, 32951280096, 225851433714, 1548008755917, 10610209857720, 72723460248138, 498454011879261, 3416454622906704, 23416728348467682

Offset: 1

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

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

Crossrefs

Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers).

Programs

Magma

[Fibonacci(4*n)-3: n in [1..50]]; // Vincenzo Librandi, Apr 20 2011

Maple

with(combinat): for n from 1 to 40 do printf(`%d,`,fibonacci(4*n)-3) od: # James Sellers, Mar 05 2003

Mathematica

Fibonacci[4Range[25]]-3 (* or *)
LinearRecurrence[{8,-8,1},{0,18,141},25] (* Paolo Xausa, Jan 07 2024 *)

Formula

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

G.f.: 3*x^2*(-6+x) / ( (x-1)*(x^2-7*x+1) ). a(n) = A033888(n)-3. - R. J. Mathar, Sep 03 2010

Extensions

More terms from James Sellers, Mar 05 2003