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 A298405 #4 Feb 10 2018 22:01:51
%S A298405 1,2,3,8,17,39,78,156,290,541,965,1718,2973,5137,8712,14741,24635,
%T A298405 41099,67998,112326,184518,302756,494904,808263,1316743,2143719,
%U A298405 3484312,5660593,9186179,14902787,24159722,39157900,63437648,102756673,166396545,269423440
%N A298405 a(n) = 2*a(n-1) - a(n-3) + a(ceiling(n/2)), where a(0) = 1, a(1) = 2, a(2) = 3.
%C A298405 a(n)/a(n-1) -> (1 + sqrt(5))/2, the golden ratio (A001622), so that (a(n)) has the growth rate of the Fibonacci numbers (A000045). See A298338 for a guide to related sequences.
%H A298405 Clark Kimberling, <a href="/A298405/b298405.txt">Table of n, a(n) for n = 0..1000</a>
%t A298405 a[0] = 1; a[1] = 2; a[2] = 3;
%t A298405 a[n_] := a[n] = 2*a[n - 1] - a[n - 3] + a[Ceiling[n/2]];
%t A298405 Table[a[n], {n, 0, 90}] (* A298405 *)
%Y A298405 Cf. A001622, A000045, A298338, A298404.
%K A298405 nonn,easy
%O A298405 0,2
%A A298405 _Clark Kimberling_, Feb 10 2018