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A298158 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) = 2, a(3) = 1. 1

%I

%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) = 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="/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) = 2, 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, 2, 1}, 100]

%Y Cf. A001622, A000045.

%K easy,sign

%O 0,2

%A _Clark Kimberling_, Feb 09 2018

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Last modified October 19 09:21 EDT 2018. Contains 316339 sequences. (Running on oeis4.)