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A298355 a(n) = a(n-1) + a(n-2) + 2 a([(n-1)/2]), where a(0) = 1, a(1) = 2, a(2) = 3.

%I A298355 #4 Feb 10 2018 09:50:25
%S A298355 1,2,3,9,16,31,53,102,173,307,512,881,1455,2442,4003,6649,10856,17851,
%T A298355 29053,47518,77185,125727,203936,331425,537123,871458,1411491,2287833,
%U A298355 3704208,6000047,9712261,15725606,25451165,41198483,66671360,107905545,174612607
%N A298355 a(n) = a(n-1) + a(n-2) + 2 a([(n-1)/2]), where a(0) = 1, a(1) = 2, a(2) = 3.
%C A298355 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 A298355 Clark Kimberling, <a href="/A298355/b298355.txt">Table of n, a(n) for n = 0..1000</a>
%t A298355 a[0] = 1; a[1] = 2; a[2] = 3;
%t A298355 a[n_] := a[n] = a[n - 1] + a[n - 2] + 2 a[Floor[(n-1)/2]];
%t A298355 Table[a[n], {n, 0, 30}]  (* A298355 *)
%Y A298355 Cf. A001622, A000045, A298338.
%K A298355 nonn,easy
%O A298355 0,2
%A A298355 _Clark Kimberling_, Feb 10 2018