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%I #7 Feb 10 2018 17:52:16
%S 1,1,1,-1,-4,-10,-8,-11,13,38,151,299,546,949,1649,2763,4204,6746,
%T 10266,16290,23536,36655,53613,83391,123900,193641,292867,460885,
%U 707580,1120644,1745334,2780325,4391131,7032724,11194491,17991105,28816020,46427283,74624283
%N a(n) = a(n-1) + a(n-2) - n*a(floor(n/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="/A298400/b298400.txt">Table of n, a(n) for n = 0..1000</a>
%t a[0] = 1; a[1] = 1; a[2] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2] - n*a[Floor[n/2]];
%t Table[a[n], {n, 0, 30}] (* A298400 *)
%Y Cf. A001622, A000045, A298338, A298401.
%K easy,sign
%O 0,5
%A _Clark Kimberling_, Feb 10 2018
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