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%I #6 Feb 10 2018 17:52:36
%S 1,2,3,7,15,30,60,112,209,373,664,1149,1985,3366,5695,9517,15877,
%T 26268,43392,71280,116956,191184,312237,508667,828135,1346018,2186735,
%U 3548701,5757079,9333118,15127052,24506542,39695843,64280511,104080748,168491921,272746723
%N a(n) = 2*a(n-1) - a(n-3) + a(floor(n/2)), where a(0) = 1, a(1) = 2, a(2) = 3.
%C 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 Clark Kimberling, <a href="/A298403/b298403.txt">Table of n, a(n) for n = 0..1000</a>
%t a[0] = 1; a[1] = 2; a[2] = 3;
%t a[n_] := a[n] = 2*a[n - 1] - a[n - 3] + a[Floor[n/2]];
%t Table[a[n], {n, 0, 90}] (* A298403 *)
%Y Cf. A001622, A000045, A298338, A298402.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, Feb 10 2018
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