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%I #8 Aug 26 2018 05:46:10
%S 27,216,868,2661,6815,15340,31324,59267,105461,178416,289332,452617,
%T 686451,1013396,1461052,2062759,2858345,3894920,5227716,6920973,
%U 9048871,11696508,14960924,18952171,23794429,29627168,36606356,44905713,54718011
%N Number of 3 X n 0..2 arrays with rows nondecreasing and antidiagonals unimodal.
%C Row 3 of A224012.
%H R. H. Hardin, <a href="/A224013/b224013.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (23/360)*n^6 + (27/40)*n^5 + (271/72)*n^4 + (65/8)*n^3 + (2101/180)*n^2 + (97/10)*n - 1 for n>1.
%F Conjectures from _Colin Barker_, Aug 26 2018: (Start)
%F G.f.: x*(27 + 27*x - 77*x^2 + 176*x^3 - 199*x^4 + 129*x^5 - 43*x^6 + 6*x^7) / (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>8.
%F (End)
%e Some solutions for n=3:
%e ..0..0..0....1..1..1....0..0..1....0..1..2....0..1..2....1..2..2....1..1..2
%e ..2..2..2....1..1..2....2..2..2....1..1..2....0..0..0....1..1..1....0..0..2
%e ..1..2..2....1..2..2....1..1..2....1..1..2....0..0..2....1..1..1....0..1..1
%Y Cf. A224012.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 30 2013
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