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A229425 Number of n X 5 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing.

%I A229425 #8 Sep 15 2018 08:45:48
%S A229425 17,102,524,2204,7816,24126,66503,166972,387738,842802,1731129,
%T A229425 3385828,6344979,11451106,19987862,33864276,55858927,89938670,
%U A229425 141669058,218736396,331604442,494332150,725582545,1049856844,1498992304
%N A229425 Number of n X 5 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing.
%H A229425 R. H. Hardin, <a href="/A229425/b229425.txt">Table of n, a(n) for n = 1..210</a>
%F A229425 Empirical: a(n) = (1/259200)*n^10 + (1/6480)*n^9 + (149/60480)*n^8 + (163/7560)*n^7 + (10411/86400)*n^6 + (1063/2160)*n^5 + (19597/12960)*n^4 + (4169/1620)*n^3 + (30649/6300)*n^2 + (215/63)*n + 4.
%F A229425 Conjectures from _Colin Barker_, Sep 15 2018: (Start)
%F A229425 G.f.: x*(17 - 85*x + 337*x^2 - 755*x^3 + 1172*x^4 - 1284*x^5 + 987*x^6 - 525*x^7 + 186*x^8 - 40*x^9 + 4*x^10) / (1 - x)^11.
%F A229425 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 A229425 (End)
%e A229425 Some solutions for n=4:
%e A229425 ..0..0..0..0..0....1..0..0..0..0....1..1..0..0..0....2..2..1..1..0
%e A229425 ..0..0..0..0..0....1..1..0..0..0....1..1..0..0..0....2..2..1..1..0
%e A229425 ..1..1..1..1..0....2..1..1..0..0....2..1..1..1..0....2..2..2..2..1
%e A229425 ..2..1..1..1..0....2..2..1..0..0....2..2..1..1..0....2..2..2..2..1
%Y A229425 Column 5 of A229428.
%K A229425 nonn
%O A229425 1,1
%A A229425 _R. H. Hardin_, Sep 22 2013