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%I #7 Sep 17 2018 08:32:08
%S 23,84,293,915,2546,6374,14536,30571,59969,110816,194535,326723,
%T 528084,825458,1252946,1853131,2678395,3792332,5271257,7205811,
%U 9702662,12886302,16900940,21912491,28110661,35711128,44957819,56125283,69521160,85488746
%N Number of 6 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.
%H R. H. Hardin, <a href="/A229449/b229449.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (2/15)*n^6 - (5/8)*n^5 + (9/2)*n^4 - (55/8)*n^3 + (283/15)*n^2 - 4*n + 11.
%F Conjectures from _Colin Barker_, Sep 17 2018: (Start)
%F G.f.: x*(23 - 77*x + 188*x^2 - 177*x^3 + 159*x^4 - 31*x^5 + 11*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=4.
%e ..0..0..0..0....0..2..2..2....0..2..2..2....0..2..2..2....0..2..2..2
%e ..0..0..0..0....1..0..2..2....0..2..2..2....1..0..2..2....1..0..2..2
%e ..0..0..0..0....2..1..0..0....0..2..2..2....1..1..0..2....1..1..0..2
%e ..1..1..1..1....2..1..0..0....1..0..2..2....2..1..0..0....1..1..1..0
%e ..2..2..2..2....2..2..1..1....1..0..2..2....2..1..0..0....2..1..1..0
%e ..2..2..2..2....2..2..2..2....1..1..0..0....2..1..0..0....2..1..1..1
%Y Row 6 of A229445.
%K nonn
%O 1,1
%A _R. H. Hardin_, Sep 23 2013
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