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%I M2431 #56 Mar 03 2024 10:39:00
%S 1,3,5,8,10,14,16,20,22,26,28,32,34,38,40,44,46,50,52,56,58,62,64,68,
%T 70,74,76,80,82,86,88,92,94,98,100,104,106,110,112,116,118,122,124,
%U 128,130,134,136,140,142,146,148,152,154,158,160,164,166
%N Davenport-Schinzel numbers of degree n on 3 symbols.
%D Annette J. Dobson and Shiela Oates Macdonald, "Lower bounds for the lengths of Davenport-Schinzel sequences", Utilitas Mathematica 6 (1974): 251-257.
%D R. K. Guy, Unsolved Problems in Number Theory, E20.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D R. G. Stanton and P. H. Dirksen, Davenport-Schinzel sequences, Ars. Combin., 1 (1976), 43-51.
%H Pankaj K. Agarwal, Micha Sharir, and Peter Shor, <a href="http://dx.doi.org/10.1016/0097-3165(89)90032-0">Sharp upper and lower bounds on the length of general Davenport-Schinzel sequences", Journal of Combinatorial Theory, Series A 52.2 (1989): 228-274.
%H Boris Aronov and Dmitriy Drusvyatskiy, <a href="http://arxiv.org/abs/1108.4336">Complexity of a Single Face in an Arrangement of s-Intersecting Curves</a>, arXiv:1108.4336v1 [cs.CG], 2011.
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H R. G. Stanton and P. H. Dirksen, <a href="/A002004/a002004.pdf">Davenport-Schinzel sequences</a>, Ars. Combin., 1 (1976), 43-51. [Annotated scanned copy]
%H R. G. Stanton and P. H. Dirksen, <a href="/A002004/a002004_1.pdf">Davenport-Schinzel sequences</a>, Ars. Combin., 1 (1976), 43-51. [Annotated scanned copy, different annotations from one above]
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, -1).
%F For n > 3, a(2*n) = 6 * n - 4 and a(2*n+1) = 6 * n - 5. - _Sean A. Irvine_, Feb 19 2016
%p A005004:=(z**3-z**2+z+1)*(z**2+z+1)/(1+z)/(z-1)**2; # Conjectured by _Simon Plouffe_ in his 1992 dissertation
%t Join[{1, 3, 5}, LinearRecurrence[{1, 1, -1}, {8, 10, 14}, 60]] (* _Jean-François Alcover_, Sep 04 2018 *)
%Y Cf. A002004.
%Y A row of the array in A259874.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
%E Improved title and more terms from _Sean A. Irvine_, Feb 19 2016
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