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%I #10 Mar 04 2024 00:20:10
%S 2,0,2,1,3,5,8,12,20,33,53,85,138,224,362,585,947,1533,2480,4012,6492,
%T 10505,16997,27501,44498,72000,116498,188497,304995,493493,798488,
%U 1291980,2090468,3382449,5472917,8855365,14328282,23183648,37511930,60695577,98207507
%N a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 2, a(1) = 0, 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="/A295689/b295689.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) = 0, a(2) = 2, a(3) = 1.
%F G.f.: (-2 + 2 x - 2 x^2 + 3 x^3)/(-1 + x + x^3 + x^4).
%t LinearRecurrence[{1, 0, 1, 1}, {2, 0, 2, 1}, 100]
%Y Cf. A001622, A000045.
%K nonn,easy
%O 0,1
%A _Clark Kimberling_, Nov 29 2017
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