login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -2, a(1) = -1, a(2) = 0, a(3) = 1.
1

%I #6 Aug 27 2021 21:06:40

%S -2,-1,0,1,7,12,31,51,106,173,327,532,955,1551,2698,4377,7459,12092,

%T 20319,32923,54778,88725,146575,237348,390067,631511,1033866,1673569,

%U 2732011,4421964,7203127,11657859,18959290,30682685,49838583,80652340,130884139

%N a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -2, a(1) = -1, a(2) = 0, 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="/A295861/b295861.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) = -1, a(2) = 0, a(3) = 1.

%F G.f.: (-2 + x + 7 x^2)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).

%t LinearRecurrence[{1, 3, -2, -2}, {-2, -1, 0, 1}, 100]

%Y Cf. A001622, A000045, A295859, A295860.

%K easy,sign

%O 0,1

%A _Clark Kimberling_, Jan 07 2018