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%I #19 Aug 27 2021 21:05:17
%S 0,0,2,1,7,6,21,23,60,75,167,226,457,651,1236,1823,3315,5010,8837,
%T 13591,23452,36531,62031,97538,163665,259155,431012,686071,1133467,
%U 1811346,2977581,4772543,7815660,12555435,20502167,32992066,53756377,86617371,140898036
%N a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, 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).
%C Therefore the terms are all >= 0. - _Georg Fischer_, Feb 19 2019
%H Clark Kimberling, <a href="/A295850/b295850.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, 3, -2, -2)
%F a(n) = a(n-1) + 3*a(n-2) - 2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = 0, a(2) = 2, a(3) = 1. [Corrected by _Colin Barker_, Dec 15 2017]
%F G.f.: -(((-2 + x) x^2)/((-1 + x + x^2) (-1 + 2 x^2))).
%F From _Colin Barker_, Dec 15 2017: (Start)
%F a(n) = -2^((n-3)/2+3/2) + ((1-sqrt(5))/2)^(n+1) + (2/(1+sqrt(5)))^(-n-1) for n even.
%F a(n) = -3*2^((n-3)/2+1) + ((1-sqrt(5))/2)^(n+1) + (2/(1+sqrt(5)))^(-n-1) for n odd.
%F (End)
%t LinearRecurrence[{1, 3, -2, -2}, {0, 0, 2, 1}, 100]
%Y Cf. A001622, A000045.
%K easy,nonn
%O 0,3
%A _Clark Kimberling_, Dec 01 2017
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