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A229439 Number of n X 2 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

%I A229439 #8 Sep 16 2018 10:10:18
%S A229439 4,7,13,25,47,84,142,228,350,517,739,1027,1393,1850,2412,3094,3912,
%T A229439 4883,6025,7357,8899,10672,12698,15000,17602,20529,23807,27463,31525,
%U A229439 36022,40984,46442,52428,58975,66117,73889,82327,91468,101350,112012,123494
%N A229439 Number of n X 2 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.
%H A229439 R. H. Hardin, <a href="/A229439/b229439.txt">Table of n, a(n) for n = 1..210</a>
%F A229439 Empirical: a(n) = (1/24)*n^4 + (1/12)*n^3 - (1/24)*n^2 + (23/12)*n + 2.
%F A229439 Conjectures from _Colin Barker_, Sep 16 2018: (Start)
%F A229439 G.f.: x*(4 - 13*x + 18*x^2 - 10*x^3 + 2*x^4) / (1 - x)^5.
%F A229439 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 A229439 (End)
%e A229439 Some solutions for n=4:
%e A229439 ..0..2....0..2....0..2....1..1....0..2....0..2....0..2....0..0....0..2....0..2
%e A229439 ..0..2....0..2....1..0....1..1....1..0....0..2....0..2....1..1....1..0....0..2
%e A229439 ..0..2....0..2....2..1....1..1....1..0....1..0....1..0....2..2....2..1....1..0
%e A229439 ..0..2....1..0....2..1....1..1....1..1....1..1....1..0....2..2....2..2....2..1
%Y A229439 Column 2 of A229445.
%K A229439 nonn
%O A229439 1,1
%A A229439 _R. H. Hardin_, Sep 23 2013