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 A298351 #4 Feb 10 2018 09:50:01
%S A298351 1,2,3,11,20,53,95,188,323,617,1046,1853,3089,5318,8783,14747,24176,
%T A298351 40157,65567,107816,175475,286997,466178,759353,1231709,2001698,
%U A298351 3244043,5263307,8524916,13817717,22372127,36238196,58658675,94977185,153716174,248824493
%N A298351 a(n) = a(n-1) + a(n-2) + 2 a(ceiling(n/2)), where a(0) = 1, a(1) = 2, a(2) = 3.
%C A298351 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 A298351 Clark Kimberling, <a href="/A298351/b298351.txt">Table of n, a(n) for n = 0..1000</a>
%t A298351 a[0] = 1; a[1] = 2; a[2] = 3;
%t A298351 a[n_] := a[n] = a[n - 1] + a[n - 2] + a[Ceiling[n/2]];
%t A298351 Table[a[n], {n, 0, 30}] (* A298351 *)
%Y A298351 Cf. A001622, A000045, A298338.
%K A298351 nonn,easy
%O A298351 0,2
%A A298351 _Clark Kimberling_, Feb 10 2018