|
%I #11 Aug 27 2021 21:21:17
%S 1,3,4,5,9,10,19,21,40,45,85,98,183,217,400,489,889,1122,2011,2621,
%T 4632,6229,10861,15042,25903,36849,62752,91409,154161,229186,383347,
%U 579765,963112,1477341,2440453,3786722,6227175,9751753,15978928,25206393,41185321
%N a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = 3, a(2) = 4, a(3) = 5.
%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="/A295718/b295718.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) = 3, a(2) = 4, a(3) = 5.
%F G.f.: (1 + 2 x - 2 x^2 - 6 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).
%t LinearRecurrence[{1, 3, -2, -2}, {1, 3, 4, 5}, 100]
%Y Cf. A001622, A000045, A005672.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, Nov 29 2017
|
