A153873 - OEIS

%I #28 Jan 03 2024 08:46:47

%S 8,17,44,116,305,800,2096,5489,14372,37628,98513,257912,675224,

%T 1767761,4628060,12116420,31721201,83047184,217420352,569213873,

%U 1490221268,3901449932,10214128529,26740935656,70008678440,183285099665,479846620556,1256254762004,3288917665457

%N a(n) = 9*Fibonacci(2n+1) - 1.

%H Vincenzo Librandi, <a href="/A153873/b153873.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,1).

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

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

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

%F a(n) = 9*A001519(n+1) - 1.

%F G.f.: (8 - 15*x + 8*x^2)/((1-x)*(1-3*x+x^2)). - _Jaume Oliver Lafont_, Aug 30 2009

%t LinearRecurrence[{4,-4,1}, {8,17,44}, 25] (* _G. C. Greubel_, Aug 31 2016 *)

%o (Magma) [9*Fibonacci(2*n+1)-1: n in [0..30]]; // _Vincenzo Librandi_, Aug 07 2011

%o (PARI) a(n)=9*fibonacci(2*n+1)-1 \\ _Charles R Greathouse IV_, Oct 07 2015

%K nonn,easy

%O 0,1

%A _Paul Curtz_, Jan 03 2009