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 A298347 #4 Feb 10 2018 09:49:38
%S A298347 1,2,3,9,18,33,69,120,225,381,672,1119,1929,3186,5355,8781,14586,
%T A298347 23817,39165,63744,104253,169341,275832,447411,727101,1178370,1911843,
%U A298347 3096585,5019138,8126433,13163133,21307128,34499433,55835733,90382800,146266167,236727297
%N A298347 a(n) = a(n-1) + a(n-2) + 2 a([n/2]), where a(0) = 1, a(1) = 2, a(2) = 3.
%C A298347 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 A298347 Clark Kimberling, <a href="/A298347/b298347.txt">Table of n, a(n) for n = 0..1000</a>
%t A298347 a[0] = 1; a[1] = 2; a[2] = 3;
%t A298347 a[n_] := a[n] = a[n - 1] + a[n - 2] + 2 a[Floor[n/2]];
%t A298347 Table[a[n], {n, 0, 30}] (* A298347 *)
%Y A298347 Cf. A001622, A000045, A298338.
%K A298347 nonn,easy
%O A298347 0,2
%A A298347 _Clark Kimberling_, Feb 10 2018