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%I #31 Sep 08 2022 08:44:46
%S 3,8,12,21,34,56,91,148,240,389,630,1020,1651,2672,4324,6997,11322,
%T 18320,29643,47964,77608,125573,203182,328756,531939,860696,1392636,
%U 2253333,3645970,5899304,9545275,15444580,24989856,40434437,65424294
%N a(n) = a(n-1) + a(n-2) + 1, with a(0)=3, a(1)=8.
%H G. C. Greubel, <a href="/A022407/b022407.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1)
%F a(n) = Fibonacci(n-2) + Fibonacci(n+5) - 1. - _Zerinvary Lajos_, Feb 01 2008
%F From Lambert Herrgesell (zero815(AT)googlemail.com), Feb 24 2008: (Start)
%F O.g.f.: (-4*x^2 + 2*x + 3)/(x^3 - 2*x + 1).
%F a(n) = -1 - B*(2/(-1-sqrt(5)))^n - C*(2/(-1+sqrt(5)))^n, with B=(-8 - 6*sqrt(5))/(5 + 3*sqrt(5)), C=(-8 + 6*sqrt(5))/(5 - 3*sqrt(5)). (End)
%p with(combinat): seq(fibonacci(n-2)+fibonacci(n+5)-1, n=0..32); # _Zerinvary Lajos_, Feb 01 2008
%t Transpose[NestList[{#[[2]],Total[#]+1}&,{3,8},35]][[1]] (* _Harvey P. Dale_, Feb 07 2011 *)
%t Table[Fibonacci[n-2] + Fibonacci[n+5] - 1, {n,0,50}] (* _G. C. Greubel_, Mar 01 2018 *)
%o (PARI) for(n=0,30, print1(fibonacci(n-2) + fibonacci(n+5) - 1, ", ")) \\ _G. C. Greubel_, Mar 01 2018
%o (Magma) [Fibonacci(n-2) + Fibonacci(n+5) - 1: n in [0..30]]; // _G. C. Greubel_, Mar 01 2018
%K nonn
%O 0,1
%A _N. J. A. Sloane_
%E More terms from _James A. Sellers_, Aug 08 2000
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