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Expansion of x - 1/(x - 1/(x - 1/(x - 1/(x + 1)))).
1

%I #16 Jun 12 2024 11:40:32

%S 1,5,10,30,85,246,707,2037,5864,16886,48620,139997,403104,1160693,

%T 3342081,9623140,27708726,79784098,229729153,661478734,1904652103,

%U 5484227157,15791202736,45468956106,130922641160,376976720745,1085461206128,3125460977225,8999406210929

%N Expansion of x - 1/(x - 1/(x - 1/(x - 1/(x + 1)))).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-1,-1).

%F a(n) = [x^n] (x^5 + x^4 - 4*x^3 - 3*x^2 + 3*x + 1)/(x^4 + x^3 - 3*x^2 - 2*x + 1).

%t CoefficientList[Series[x - 1/(x - 1/(x - 1/(x - 1/(x + 1)))), {x, 0, 28}], x] (* _Michael De Vlieger_, Jun 10 2024 *)

%Y Essentially the same as A006357.

%K nonn,easy

%O 0,2

%A _Peter Luschny_, Jun 10 2024