A295736 - OEIS

%I #6 Aug 27 2021 21:03:55

%S 1,-2,-2,1,-3,8,1,29,22,91,97,268,333,761,1030,2111,3013,5764,8521,

%T 15565,23574,41699,64249,111068,173269,294577,463750,778807,1234365,

%U 2054132,3272113,5408165,8647510,14219515,22801489,37348684,60019101,98023145,157780102

%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="/A295736/b295736.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 - 3 x - 3 x^2 + 11 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, A005672.

%K easy,sign

%O 0,2

%A _Clark Kimberling_, Nov 30 2017