%I #7 Aug 27 2021 21:15:31
%S 0,0,3,1,10,7,29,28,81,93,222,283,601,820,1613,2305,4302,6351,11421,
%T 17260,30217,46453,79742,124147,210033,330084,552405,874297,1451278,
%U 2309191,3809621,6086044,9993969,16014477,26205054,42088459,68686729,110513044
%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) = 3, 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="/A295856/b295856.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) + a(n-3) + a(n-4), where a(0) = 0, a(1) = 0, a(2) = 3, a(3) = 1.
%F G.f.: ((3 - 2 x) x^2)/((-1 + x + x^2) (-1 + 2 x^2)).
%t LinearRecurrence[{1, 3, -2, -2}, {0, 0, 3, 1}, 100]
%Y Cf. A001622, A000045.
%K nonn,easy
%O 0,3
%A _Clark Kimberling_, Dec 01 2017