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%I #6 Feb 10 2018 17:52:23
%S 1,2,3,-1,-10,-26,-30,-49,1,42,303,631,1294,2315,4295,7345,11624,
%T 18952,29820,47974,71734,113345,171197,270029,410170,647849,997829,
%U 1583173,2460742,3919360,6159752,9851417,15639201,25107026,40101859,64545565,103573904
%N a(n) = a(n-1) + a(n-2) - n*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="/A298401/b298401.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] = a[n - 1] + a[n - 2] - n*a[Floor[n/2]];
%t Table[a[n], {n, 0, 30}] (* A298401 *)
%Y Cf. A001622, A000045, A298338, A298400.
%K easy,sign
%O 0,2
%A _Clark Kimberling_, Feb 10 2018
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