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A298352 a(n) = a(n-1) + a(n-2) + a([(n-1)/2]), where a(0) = 1, a(1) = 1, a(2) = 1.

%I A298352 #8 Nov 06 2018 13:16:23
%S A298352 1,1,1,3,5,9,15,27,45,77,127,213,349,577,941,1545,2513,4103,6661,
%T A298352 10841,17579,28547,46253,75013,121479,196841,318669,516087,835333,
%U A298352 1352361,2188635,3542541,5732721,9277775,15013009,24294887,39311999,63613547,102932207
%N A298352 a(n) = a(n-1) + a(n-2) + a([(n-1)/2]), where a(0) = 1, a(1) = 1, a(2) = 1.
%C A298352 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 A298352 Clark Kimberling, <a href="/A298352/b298352.txt">Table of n, a(n) for n = 0..1000</a>
%t A298352 a[0] = 1; a[1] = 1; a[2] = 1;
%t A298352 a[n_] := a[n] = a[n - 1] + a[n - 2] + a[Floor[(n-1)/2]];
%t A298352 Table[a[n], {n, 0, 30}]  (* A298352 *)
%Y A298352 Cf. A001622, A000045, A298338.
%K A298352 nonn,easy
%O A298352 0,4
%A A298352 _Clark Kimberling_, Feb 10 2018