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A201695 Number of n X 3 0..2 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.

%I A201695 #9 May 23 2018 20:03:39
%S A201695 3,18,116,395,989,2068,3838,6541,10455,15894,23208,32783,45041,60440,
%T A201695 79474,102673,130603,163866,203100,248979,302213,363548,433766,513685,
%U A201695 604159,706078,820368,947991,1089945,1247264,1421018,1612313,1822291
%N A201695 Number of n X 3 0..2 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.
%C A201695 Column 3 of A201700.
%H A201695 R. H. Hardin, <a href="/A201695/b201695.txt">Table of n, a(n) for n = 1..210</a>
%F A201695 Empirical: a(n) = (3/2)*n^4 + (4/3)*n^3 - 4*n^2 - (29/6)*n + 9.
%F A201695 Conjectures from _Colin Barker_, May 23 2018: (Start)
%F A201695 G.f.: x*(3 + 3*x + 56*x^2 - 35*x^3 + 9*x^4) / (1 - x)^5.
%F A201695 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F A201695 (End)
%e A201695 Some solutions for n=4:
%e A201695 ..1..2..2....0..0..1....0..2..2....0..2..2....1..1..2....0..0..2....0..0..2
%e A201695 ..1..2..2....0..2..0....2..0..1....1..1..2....1..2..1....0..2..0....0..1..0
%e A201695 ..2..1..2....0..2..0....2..0..1....1..2..0....2..0..1....2..0..0....2..0..0
%e A201695 ..2..2..0....2..0..0....2..1..0....2..0..0....2..1..0....2..0..0....2..0..0
%Y A201695 Cf. A201700.
%K A201695 nonn
%O A201695 1,1
%A A201695 _R. H. Hardin_, Dec 03 2011