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

1,2

References

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

Links

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

Maple

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A212154 A108680 A204273 * A299062 A299723 A125355

Adjacent sequences: A081071 A081072 A081073 * A081075 A081076 A081077

Keyword

nonn,easy

Author

R. K. Guy, Mar 04 2003

Extensions

More terms from James A. Sellers, Mar 05 2003

Status

approved