|
%I #6 Aug 27 2021 21:22:41
%S 2,1,0,2,5,6,8,15,26,40,63,104,170,273,440,714,1157,1870,3024,4895,
%T 7922,12816,20735,33552,54290,87841,142128,229970,372101,602070,
%U 974168,1576239,2550410,4126648,6677055,10803704,17480762,28284465,45765224,74049690
%N a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 2, a(1) = 1, a(2) = 0, a(3) = 2.
%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="/A295688/b295688.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) = 2, a(1) = 1, a(2) = 0, a(3) = 1.
%F G.f.: (-2 + x + x^2)/(-1 + x + x^3 + x^4).
%t LinearRecurrence[{1, 0, 1, 1}, {2, 1, 0, 2}, 100]
%Y Cf. A001622, A000045.
%K nonn,easy
%O 0,1
%A _Clark Kimberling_, Nov 29 2017
|
