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 A298341 #4 Feb 09 2018 21:50:05
%S A298341 1,2,3,7,12,21,36,60,99,166,272,445,729,1186,1927,3134,5082,8237,
%T A298341 13355,21628,35019,56707,91786,148553,240438,389090,629627,1018883,
%U A298341 1648676,2667725,4316673,6984670,11301615,18286730,29588790,47875965,77465484,125342178
%N A298341 a(n) = a(n-1) + a(n-2) + a([n/3]), where a(0) = 1, a(1) = 2, a(2) = 3.
%C A298341 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 A298341 Clark Kimberling, <a href="/A298341/b298341.txt">Table of n, a(n) for n = 0..1000</a>
%t A298341 a[0] = 1; a[1] = 2; a[2] = 3;
%t A298341 a[n_] := a[n] = a[n - 1] + a[n - 2] + a[Floor[n/3]];
%t A298341 Table[a[n], {n, 0, 30}] (* A298341 *)
%Y A298341 Cf. A001622, A000045, A298338.
%K A298341 nonn,easy
%O A298341 0,2
%A A298341 _Clark Kimberling_, Feb 09 2018