This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A049658 #18 Nov 28 2024 15:16:25
%S A049658 1,77,3648,171409,8052605,378301056,17772097057,834910260653,
%T A049658 39223010153664,1842646566961585,86565165637040861,
%U A049658 4066720138373958912,191049281337939028033,8975249502744760358669
%N A049658 a(n) = (F(8*n+5) - 2)/3, where F = A000045 (the Fibonacci sequence).
%H A049658 G. C. Greubel, <a href="/A049658/b049658.txt">Table of n, a(n) for n = 0..595</a>
%H A049658 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (48, -48, 1).
%F A049658 G.f.: (1+29*x)/(1-48*x+48*x^2-x^3).
%F A049658 a(0)=1, a(1)=77, a(2)=3648, a(n) = 48*a(n-1)-48*a(n-2)+a(n-3). - _Harvey P. Dale_, Jun 20 2013
%F A049658 Product_{n>=1} (1 - 1/a(n)) = 3*(5+sqrt(5))/22 = (15/11) * A242671. - _Amiram Eldar_, Nov 28 2024
%t A049658 (Fibonacci[8Range[0,20]+5]-2)/3 (* or *) LinearRecurrence[{48,-48,1},{1,77,3648},20] (* _Harvey P. Dale_, Jun 20 2013 *)
%o A049658 (PARI) for(n=0,30, print1((fibonacci(8*n+5) - 2)/3, ", ")) \\ _G. C. Greubel_, Dec 02 2017
%o A049658 (Magma) [(Fibonacci(8*n+5) - 2)/3: n in [0..30]]; // _G. C. Greubel_, Dec 02 2017
%Y A049658 Cf. A000045, A242671.
%K A049658 nonn
%O A049658 0,2
%A A049658 _Clark Kimberling_
%E A049658 Description corrected by and more terms from _Michael Somos_