%I #8 May 23 2018 16:39:35
%S 3,27,395,4998,35390,167625,607919,1826778,4775228,11211034,24167306,
%T 48600665,92261185,166831642,289389192,484248471,785251265,1238574341,
%U 1906133765,2869671064,4235613920,6140811719,8759254221,12309889872
%N Number of n X 4 0..2 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.
%C Column 4 of A201700.
%H R. H. Hardin, <a href="/A201696/b201696.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/907200)*n^10 + (13/20160)*n^9 + (8321/120960)*n^8 + (97/105)*n^7 - (40969/5400)*n^6 + (22681/960)*n^5 - (11661313/362880)*n^4 - (388097/10080)*n^3 + (4320179/16800)*n^2 - (323861/840)*n + 185.
%F Conjectures from _Colin Barker_, May 23 2018: (Start)
%F G.f.: x*(3 - 6*x + 263*x^2 + 1643*x^3 - 1328*x^4 - 4426*x^5 + 5086*x^6 - 1972*x^7 + 1789*x^8 - 1233*x^9 + 185*x^10) / (1 - x)^11.
%F a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.
%F (End)
%e Some solutions for n=3:
%e ..0..1..1..2....0..1..1..2....0..1..1..1....0..1..2..2....0..1..2..2
%e ..1..0..0..2....2..1..1..0....2..0..0..0....0..2..0..0....0..2..1..2
%e ..2..2..2..0....2..1..1..0....2..0..0..0....1..0..0..0....2..1..1..0
%Y Cf. A201700.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 03 2011