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%I #8 Aug 29 2018 05:57:48
%S 22,158,684,2205,5852,13524,28176,54153,97570,166738,272636,429429,
%T 655032,971720,1406784,1993233,2770542,3785446,5092780,6756365,
%U 8849940,11458140,14677520,18617625,23402106,29169882,36076348,44294629,54016880
%N Number of n X 3 0..2 arrays with rows unimodal and columns nondecreasing.
%C Column 3 of A224190.
%H R. H. Hardin, <a href="/A224185/b224185.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (23/360)*n^6 + (27/40)*n^5 + (205/72)*n^4 + (49/8)*n^3 + (319/45)*n^2 + (21/5)*n + 1.
%F Conjectures from _Colin Barker_, Aug 29 2018: (Start)
%F G.f.: x*(22 + 4*x + 40*x^2 - 35*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F (End)
%e Some solutions for n=3.
%e ..1..0..0....0..1..0....2..1..0....0..2..1....0..0..0....0..0..1....0..0..0
%e ..2..0..0....1..2..0....2..2..0....0..2..1....1..0..0....0..0..2....1..1..0
%e ..2..0..0....1..2..2....2..2..1....1..2..1....2..2..0....0..0..2....2..2..0
%Y Cf. A224190.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 01 2013
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