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%I #10 Feb 20 2019 08:10:00
%S 3,5,5,8,12,8,12,27,27,12,17,55,83,55,17,23,102,222,222,102,23,30,175,
%T 524,754,524,175,30,38,282,1116,2204,2204,1116,282,38,47,432,2187,
%U 5700,7816,5700,2187,432,47,57,635,4005,13345,24126,24126,13345,4005,635,57
%N T(n,k) = Number of n X k 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing.
%C Table starts
%C ..3...5....8....12.....17.....23......30.......38.......47........57........68
%C ..5..12...27....55....102....175.....282......432......635.......902......1245
%C ..8..27...83...222....524...1116....2187.....4005.....6936.....11465.....18219
%C .12..55..222...754...2204...5700...13345....28794....58053....110550....200533
%C .17.102..524..2204...7816..24126...66503...166972...387738....842802...1731129
%C .23.175.1116..5700..24126..87648..281016...812352..2152643...5297329..12231874
%C .30.282.2187.13345..66503.281016.1037193..3420692.10260128..28379127..73192023
%C .38.432.4005.28794.166972.812352.3420692.12768612.43042290.132960319.380811699
%H R. H. Hardin, <a href="/A229428/b229428.txt">Table of n, a(n) for n = 1..480</a>
%F Empirical for column k:
%F k=1: a(n) = (1/2)*n^2 + (1/2)*n + 2
%F k=2: a(n) = (1/24)*n^4 + (5/12)*n^3 + (11/24)*n^2 + (25/12)*n + 2, A229422
%F k=3: [polynomial of degree 6], A229423
%F k=4: [polynomial of degree 8], A229424
%F k=5: [polynomial of degree 10], A229425
%F k=6: [polynomial of degree 12], A229426
%F k=7: [polynomial of degree 14]
%e Some solutions for n=4 k=4
%e ..2..2..1..0....1..1..0..0....1..1..0..0....2..1..1..1....1..0..0..0
%e ..2..2..1..1....2..1..0..0....2..1..0..0....2..1..1..1....1..1..1..1
%e ..2..2..1..1....2..1..1..1....2..1..1..1....2..2..2..1....2..2..1..1
%e ..2..2..2..1....2..1..1..1....2..2..1..1....2..2..2..2....2..2..2..1
%Y Column 1 is A022856(n+4).
%Y Main diagonal is A229421.
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Sep 22 2013
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