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%I #17 Oct 24 2023 18:54:31
%S 0,2,3,4,6,10,17,30,54,98,179,328,602,1106,2033,3738,6874,12642,23251,
%T 42764,78654,144666,266081,489398,900142,1655618,3045155,5600912,
%U 10301682,18947746,34850337,64099762,117897842,216847938,398845539,733591316,1349284790,2481721642
%N Expansion of g.f. -x*(2*x^3+2*x^2+x-2)/(x^4-2*x+1).
%C a(n) = length of A317199(n).
%H Andrew Howroyd, <a href="/A317200/b317200.txt">Table of n, a(n) for n = 1..1000</a>
%H Bo Tan and Zhi-Ying Wen, <a href="http://dx.doi.org/10.1016/j.ejc.2006.07.007">Some properties of the Tribonacci sequence</a>, European Journal of Combinatorics, 28 (2007) 1703-1719. See Prop. 2.9.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,-1).
%F Bo Tan et al. express a(n) in terms of the tribonacci numbers A000073.
%t CoefficientList[Series[-x(2x^3+2x^2+x-2)/(x^4-2x+1),{x,0,40}],x] (* _Harvey P. Dale_, Aug 31 2020 *)
%o (PARI) my(N=40); Vec(x*(2 - x - 2*x^2 - 2*x^3)/((1 - x)*(1 - x - x^2 - x^3)) + O(x^N), -N) \\ _Andrew Howroyd_, Oct 24 2023
%Y Cf. A000073, A317199.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Aug 05 2018
%E Zero prepended by _Harvey P. Dale_, Aug 31 2020
%E a(36)-a(38) from _Stefano Spezia_, Oct 24 2023
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