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%I #35 Aug 03 2022 07:03:50
%S 1,14,69,203,463,903,1585,2579,3963,5823,8253,11355,15239,20023,25833,
%T 32803,41075,50799,62133,75243,90303,107495,127009,149043,173803,
%U 201503,232365,266619,304503,346263,392153,442435,497379,557263,622373,693003,769455,852039
%N Number of Baxter matrices of size 3 X n.
%H Michael S. Branicky, <a href="/A347673/b347673.txt">Table of n, a(n) for n = 1..65</a>
%H George Spahn, <a href="https://arxiv.org/abs/2110.09688">Counting Baxter Matrices</a>, arXiv:2110.09688 [math.CO], 2021.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F From _George Spahn_, Oct 20 2021: (Start)
%F a(n) = 1/3*n^4 + 3*n^3 - 16/3*n^2 + 2*n + 3 for n >= 3.
%F G.f.: -x*(x^6 - 3*x^5 + 3*x^4 - 12*x^3 + 9*x^2 + 9*x + 1)/(x - 1)^5. (End)
%t Rest@ CoefficientList[Series[-x (x^6 - 3 x^5 + 3 x^4 - 12 x^3 + 9 x^2 + 9 x + 1)/(x - 1)^5, {x, 0, 38}], x] (* _Michael De Vlieger_, Oct 20 2021 *)
%Y Row 3 of A347672.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Sep 10 2021
%E a(8)-a(38) from _Michael S. Branicky_, Sep 13 2021