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%I #4 Feb 10 2018 09:50:18
%S 1,1,1,4,7,13,22,43,73,130,217,373,616,1033,1693,2812,4591,7549,12286,
%T 20095,32641,53170,86245,140161,227152,368545,596929,967540,1566535,
%U 2537461,4107382,6650467,10763473,17423122,28195777,45633997,73844872,119503441
%N a(n) = a(n-1) + a(n-2) + 2 a([(n-1)/2]), where a(0) = 1, a(1) = 1, a(2) = 1.
%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="/A298354/b298354.txt">Table of n, a(n) for n = 0..1000</a>
%t a[0] = 1; a[1] = 1; a[2] = 1;
%t a[n_] := a[n] = a[n - 1] + a[n - 2] + 2 a[Floor[(n-1)/2]];
%t Table[a[n], {n, 0, 30}] (* A298354 *)
%Y Cf. A001622, A000045, A298338.
%K nonn,easy
%O 0,4
%A _Clark Kimberling_, Feb 10 2018
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