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 A111365 #18 Jan 01 2024 11:38:29
%S A111365 1,1,8,43,239,1324,7337,40657,225296,1248451,6918143,38336068,
%T A111365 212434769,1177182049,6523214552,36147618907,200307738191,
%U A111365 1109981547676,6150830952953,34084099407793,188872989897824,1046617247712499
%N A111365 a(n) = 5*a(n-1) + 3*a(n-2) where a(0) = a(1) = 1.
%D A111365 Thomas Koshy, "Fibonacci and Lucas Numbers with Applications", Wiley, 2001
%H A111365 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5, 3).
%F A111365 a(n)=A015536(n+1)-4*A015536(n). G.f.: (1-4x)/(1-5x-3x^2). [From _R. J. Mathar_, Jul 08 2009]
%e A111365 a(2) = 5*a(1) + 3*a(0) = 5*1 + 3*1 = 8 which is the third term in the sequence.
%t A111365 Transpose[NestList[Flatten[{Rest[#],ListCorrelate[{3,5},#]}]&, {1,1},40]][[1]] (* _Harvey P. Dale_, Mar 23 2011 *)
%Y A111365 Cf. A000045, A072264.
%K A111365 nonn
%O A111365 0,3
%A A111365 _Parthasarathy Nambi_, Nov 07 2005
%E A111365 More terms from _Robert G. Wilson v_, Nov 10 2005