%I #6 Aug 27 2021 21:20:59
%S 1,4,9,16,33,55,104,171,307,502,873,1423,2424,3943,6623,10758,17893,
%T 29035,47952,77755,127755,207046,338897,549015,896104,1451263,2363751,
%U 3827302,6223821,10075699,16365056,26489907,42986035,69574246,112822425,182593279
%N a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = 4, a(2) = 9, a(3) = 16.
%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="/A295720/b295720.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) = 1, a(1) = 4, a(2) = 9, a(3) = 16.
%F G.f.: (1 + 3 x + 2 x^2 - 3 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).
%t LinearRecurrence[{1, 3, -2, -2}, {1, 4, 9, 16}, 100]
%Y Cf. A001622, A000045, A005672.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, Nov 29 2017