|
%I #6 Aug 27 2021 21:06:59
%S -2,0,1,1,8,9,29,38,91,129,268,397,761,1158,2111,3269,5764,9033,15565,
%T 24598,41699,66297,111068,177365,294577,471942,778807,1250749,2054132,
%U 3304881,5408165,8713046,14219515,22932561,37348684,60281245,98023145,158304390
%N a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -2, a(1) = 0, 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="/A295859/b295859.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) = -2, a(1) = 0, a(2) = 1, a(3) = 1.
%F G.f.: (-2 + 2 x + 7 x^2 - 4 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).
%t LinearRecurrence[{1, 3, -2, -2}, {-2, 0, 1, 1}, 100]
%Y Cf. A001622, A000045, A295860.
%K easy,sign
%O 0,1
%A _Clark Kimberling_, Jan 07 2018
|
