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 A298350 #4 Feb 10 2018 09:49:55
%S A298350 1,1,1,4,7,19,34,67,115,220,373,661,1102,1897,3133,5260,8623,14323,
%T A298350 23386,38455,62587,102364,166273,270841,439318,713953,1157065,1877284,
%U A298350 3040615,4928419,7979554,12925219,20922019,33875884,54826549,88749205,143622526
%N A298350 a(n) = a(n-1) + a(n-2) + 2 a(ceiling(n/2)), where a(0) = 1, a(1) = 1, a(2) = 1.
%C A298350 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 A298350 Clark Kimberling, <a href="/A298350/b298350.txt">Table of n, a(n) for n = 0..1000</a>
%t A298350 a[0] = 1; a[1] = 1; a[2] = 1;
%t A298350 a[n_] := a[n] = a[n - 1] + a[n - 2] + a[Ceiling[n/2]];
%t A298350 Table[a[n], {n, 0, 30}] (* A298350 *)
%Y A298350 Cf. A001622, A000045, A298338.
%K A298350 nonn,easy
%O A298350 0,4
%A A298350 _Clark Kimberling_, Feb 10 2018