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A298348 a(n) = a(n-1) + a(n-2) + a([(n+1)/2]), where a(0) = 1, a(1) = 1, a(2) = 1.

%I A298348 #4 Feb 10 2018 09:49:43
%S A298348 1,1,1,3,5,11,19,35,59,105,175,299,493,827,1355,2241,3655,6001,9761,
%T A298348 15937,25873,42109,68281,110883,179657,291367,471851,764573,1237779,
%U A298348 2004593,3244613,5252861,8501129,13759991,22267121,36036873,58313755,94366565,152696257
%N A298348 a(n) = a(n-1) + a(n-2) + a([(n+1)/2]), where a(0) = 1, a(1) = 1, a(2) = 1.
%C A298348 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 A298348 Clark Kimberling, <a href="/A298348/b298348.txt">Table of n, a(n) for n = 0..1000</a>
%t A298348 a[0] = 1; a[1] = 1; a[2] = 1;
%t A298348 a[n_] := a[n] = a[n - 1] + a[n - 2] + a[Floor[(n+1)/2]];
%t A298348 Table[a[n], {n, 0, 30}]  (* A298348 *)
%Y A298348 Cf. A001622, A000045, A298338.
%K A298348 nonn,easy
%O A298348 0,4
%A A298348 _Clark Kimberling_, Feb 10 2018