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 A049661 #38 Nov 28 2024 15:02:49
%S A049661 0,3,58,1045,18756,336567,6039454,108373609,1944685512,34895965611,
%T A049661 626182695490,11236392553213,201628883262348,3618083506169055,
%U A049661 64923874227780646,1165011652593882577,20905285872462105744
%N A049661 a(n) = (Fibonacci(6*n+1) - 1)/4.
%H A049661 G. C. Greubel, <a href="/A049661/b049661.txt">Table of n, a(n) for n = 0..750</a> (terms 0..100 from Vincenzo Librandi)
%H A049661 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (19,-19,1).
%F A049661 From _R. J. Mathar_, Nov 04 2008: (Start)
%F A049661 G.f.: x*(3+x)/((1-x)*(1-18*x+x^2)).
%F A049661 a(n) = 19*a(n-1) - 19*a(n-2) + a(n-3). (End)
%F A049661 a(n) = (-1/4+1/40*(9+4*sqrt(5))^(-n)*(5-sqrt(5)+(5+sqrt(5))*(9+4*sqrt(5))^(2*n))). - _Colin Barker_, Mar 03 2016
%F A049661 Product_{n>=1} (1 - 1/a(n)) = (sqrt(5)+3)/8 = phi^2/4 = cos(Pi/5)^2 = A019863^2 = (A374149 + 1)/10. - _Amiram Eldar_, Nov 28 2024
%t A049661 Table[(Fibonacci[6n+1]-1)/4,{n,0,20}] (* or *) LinearRecurrence[ {19,-19,1},{0,3,58},20] (* _Harvey P. Dale_, Aug 22 2011 *)
%o A049661 (Magma) [(Fibonacci(6*n+1)-1)/4: n in [0..20] ]; // _Vincenzo Librandi_, Aug 23 2011
%o A049661 (PARI) a(n)=fibonacci(6*n+1)>>2 \\ _Charles R Greathouse IV_, Aug 23 2011
%Y A049661 Cf. A000045, A019863, A374149.
%K A049661 nonn,easy
%O A049661 0,2
%A A049661 _Clark Kimberling_