%I #24 Sep 08 2022 08:46:21

%S 1,3,5,11,23,53,125,307,769,1959,5039,13049,33929,88451,230957,603667,

%T 1578823,4130829,10810469,28295411,74067401,193893263,507590495,

%U 1328842801,3478880593,9107706243,23844088085,62424315227,163428464759,427860443429,1120151837069

%N a(n) = F(n)*F(n+1) + F(n+2), where F = A000045 (Fibonacci numbers).

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-5,-1,1).

%F G.f.: (1 - 5*x^2 - 2*x^3 + x^4)/((x + 1)*(1 - 3*x + x^2)*(1 - x - x^2)).

%F a(n) = 3*a(n-1) + a(n-2) - 5*a(n-3) - a(n-4) + a(n-5).

%F 5*a(n) = (-1)^(n+1) +5*F(n+2) + A002878(n). - _R. J. Mathar_, Nov 14 2019

%t Table[Fibonacci[n] Fibonacci[n+1] + Fibonacci[n+2], {n, 0, 30}]

%o (Magma) [Fibonacci(n)*Fibonacci(n+1)+Fibonacci(n+2): n in [0..30]];

%o (GAP) List([0..35], n -> Fibonacci(n)*Fibonacci(n+1)+Fibonacci(n+2)); # _Muniru A Asiru_, Jun 06 2018

%Y Cf. A001654, A269803.

%Y Cf. A059769: F(n)*F(n+1) - F(n+2), with offset 3.

%Y Equals A000045 + A286983.

%Y First differences are listed in A059727 (after 0).

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, Jun 05 2018