A295680 - OEIS

%I #6 Nov 28 2017 10:30:53

%S 0,0,0,2,2,2,4,8,12,18,30,50,80,128,208,338,546,882,1428,2312,3740,

%T 6050,9790,15842,25632,41472,67104,108578,175682,284258,459940,744200,

%U 1204140,1948338,3152478,5100818,8253296,13354112,21607408,34961522,56568930

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

%C Lim_{n->inf} 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="/A295680/b295680.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, 0, 1, 1)

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

%F a(n) = 2*A006498(n-3) for n >= 3.

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

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

%Y Cf. A001622, A000045.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, Nov 27 2017