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%I #10 Aug 27 2021 21:06:29
%S -1,-2,1,1,10,15,41,64,137,217,418,667,1213,1944,3413,5485,9410,15151,
%T 25585,41248,68881,111153,184130,297331,489653,791080,1297117,2096389,
%U 3426274,5539047,9030857,14602672,23764601,38432809,62459554,101023435,164007277
%N a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = -2, a(2) = 1, 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="/A298158/b298158.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) = -2, a(2) = 1, a(3) = 1.
%F G.f.: (-1 - x + 6 x^2 + 4 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).
%t LinearRecurrence[{1, 3, -2, -2}, {-1, -2, 1, 1}, 37] (* corrected by _Georg Fischer_, Apr 03 2019 *)
%o (PARI) x='x+O('x^37); Vec((-1 - x + 6*x^2 + 4*x^3)/(1 - x - 3*x^2 + 2*x^3 + 2*x^4)) \\ _Georg Fischer_, Apr 03 2019
%Y Cf. A001622, A000045.
%K easy,sign
%O 0,2
%A _Clark Kimberling_, Feb 09 2018
%E a(2)=1 corrected by _Georg Fischer_, Apr 03 2019
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