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 A293411 #23 Jul 20 2025 10:52:04
%S A293411 1,2,3,4,7,12,19,30,49,80,129,208,337,546,883,1428,2311,3740,6051,
%T A293411 9790,15841,25632,41473,67104,108577,175682,284259,459940,744199,
%U A293411 1204140,1948339,3152478,5100817,8253296,13354113,21607408,34961521,56568930,91530451
%N A293411 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 2, a(2) = 3, a(3) = 4.
%C A293411 a(n)/a(n-1) -> (1 + sqrt(5))/2 = golden ratio (A001622), so that this sequence has the growth rate of the Fibonacci numbers (A000045).
%H A293411 Clark Kimberling, <a href="/A293411/b293411.txt">Table of n, a(n) for n = 0..1999</a>
%H A293411 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,1).
%F A293411 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 2, a(2) = 3, a(3) = 4.
%F A293411 G.f.: (1+x+x^2)/((1+x^2)*(1-x-x^2)).
%F A293411 From _Greg Dresden_, Aug 25 2021: (Start)
%F A293411 a(2*n) = a(2*n - 1) + a(2*n - 2),
%F A293411 a(2*n) = 2*F(n+1)^2 - (-1)^n = A061646(n+1),
%F A293411 a(2*n+1) = 2*F(n+1)*F(n+2) = A079472(n+2), for F(n) the Fibonacci numbers A000045. (End)
%F A293411 a(n) = round (2*A000032(n+2)/5). - _R. J. Mathar_, Jul 20 2025
%t A293411 LinearRecurrence[{1, 0, 1, 1}, {1, 2, 3, 4}, 100]
%Y A293411 Cf. A001622, A000045, A295619, A295620, A061646, A079472.
%K A293411 nonn,easy
%O A293411 0,2
%A A293411 _Clark Kimberling_, Nov 25 2017