A295681 - OEIS

%I #6 Nov 28 2017 10:31:00

%S 0,1,0,2,3,4,6,11,18,28,45,74,120,193,312,506,819,1324,2142,3467,5610,

%T 9076,14685,23762,38448,62209,100656,162866,263523,426388,689910,

%U 1116299,1806210,2922508,4728717,7651226,12379944,20031169,32411112,52442282,84853395

%N a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 0, a(1) = 1, 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="/A295681/b295681.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) = 1, a(2) = 0, a(3) = 2.

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

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

%Y Cf. A001622, A000045.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, Nov 27 2017