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%I M3928 #21 Nov 07 2017 18:15:42
%S 5,24,79,223,579,1432,3434,8071,18714,42991,98127,222965,505008,
%T 1141236,2574845,5802636,13065935,29403439,66141015,148734156,
%U 334391354,751675943,1689494650,3797059555,8533209055,19176039925,43091557504,96831330948,217586892705
%N Total preorders.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Colin Barker, <a href="/A006328/b006328.txt">Table of n, a(n) for n = 3..1000</a>
%H G. Kreweras, <a href="http://www.numdam.org/item?id=MSH_1976__53__5_0">Les préordres totaux compatibles avec un ordre partiel</a>, Math. Sci. Humaines No. 53 (1976), 5-30.
%H G. Kreweras, <a href="/A019538/a019538.pdf">Les préordres totaux compatibles avec un ordre partiel</a>, Math. Sci. Humaines No. 53 (1976), 5-30. (Annotated scanned copy)
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,-4,4,1,-1).
%F From _Colin Barker_, Mar 19 2017: (Start)
%F G.f.: x^3*(1 + x)*(5 - x - x^2) / ((1 - x)*(1 - x - x^2)*(1 - 2*x - x^2 + x^3)).
%F a(n) = 4*a(n-1) - 3*a(n-2) - 4*a(n-3) + 4*a(n-4) + a(n-5) - a(n-6) for n>8.
%F (End)
%t CoefficientList[ Series[(5 + 4x - 2x^2 - x^3)/(1 - 4x + 3x^2 + 4x^3 - 4 x^4 - x^5 + x^6), {x, 0, 30}], x] (* _Robert G. Wilson v_, Mar 12 2017 *)
%o (PARI) Vec(x^3*(1 + x)*(5 - x - x^2) / ((1 - x)*(1 - x - x^2)*(1 - 2*x - x^2 + x^3)) + O(x^40)) \\ _Colin Barker_, Mar 19 2017
%Y A column of A079502.
%K nonn,easy
%O 3,1
%A _N. J. A. Sloane_
%E More terms from _Sean A. Irvine_, Mar 12 2017