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 A111573 #36 Feb 07 2025 00:35:15
%S A111573 0,1,3,3,4,8,14,21,33,55,90,144,232,377,611,987,1596,2584,4182,6765,
%T A111573 10945,17711,28658,46368,75024,121393,196419,317811,514228,832040,
%U A111573 1346270,2178309,3524577,5702887,9227466,14930352,24157816,39088169
%N A111573 a(n) = a(n-1) + a(n-3) + a(n-4), n >= 4, with initial terms 0,1,3,3.
%C A111573 See comment and FAMP code for A111569.
%H A111573 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,1).
%F A111573 G.f.: -x*(1+2*x)/((x^2+x-1)*(x^2+1)).
%F A111573 a(n) = A056594(n+3) + A000045(n+1). - _R. J. Mathar_, Nov 10 2009
%F A111573 From _Greg Dresden_, Jan 15 2024: (Start)
%F A111573 a(2*n) = Fibonacci(n)*Lucas(n+1);
%F A111573 a(2*n+1) = Fibonacci(2*n+1). (End)
%t A111573 Table[Fibonacci[n + 1] - Cos[n*Pi/2], {n, 0, 40}] (* _Greg Dresden_, Oct 16 2021 *)
%Y A111573 Cf. A001638, A111569, A111570, A111571, A111572, A111574, A111575, A111576.
%K A111573 easy,nonn
%O A111573 0,3
%A A111573 _Creighton Dement_, Aug 10 2005
%E A111573 Name clarified by _Robert C. Lyons_, Feb 06 2025