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%I #6 Aug 27 2021 21:21:40
%S 2,2,2,1,5,9,12,18,32,53,83,133,218,354,570,921,1493,2417,3908,6322,
%T 10232,16557,26787,43341,70130,113474,183602,297073,480677,777753,
%U 1258428,2036178,3294608,5330789,8625395,13956181,22581578,36537762,59119338,95657097
%N a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 2, a(1) = 2, a(2) = 2, a(3) = 1.
%C a(n)/a(n-1) -> (1 + sqrt(5))/2 = golden ratio (A001622), so that a( ) has the growth rate of the Fibonacci numbers (A000045).
%H Clark Kimberling, <a href="/A295691/b295691.txt">Table of n, a(n) for n = 0..2000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 1, 1)
%F a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 2, a(1) = 2, a(2) = 2, a(3) = 1.
%F G.f.: (-2 + 3 x^3)/(-1 + x + x^3 + x^4).
%t LinearRecurrence[{1, 0, 1, 1}, {2, 2, 2, 1}, 100]
%Y Cf. A001622, A000045.
%K nonn,easy
%O 0,1
%A _Clark Kimberling_, Nov 29 2017
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