|
%I #8 Sep 17 2018 08:31:33
%S 6,14,37,109,324,915,2402,5843,13229,28071,56234,107080,194989,341334,
%T 576993,945488,1506848,2342300,3559899,5301215,7749202,11137381,
%U 15760476,21986649,30271487,41173901,55374104,73693842,97119059,126825184
%N Number of n X 4 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="/A229441/b229441.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/5760)*n^8 + (1/2016)*n^7 + (1/576)*n^6 + (11/360)*n^5 + (409/5760)*n^4 + (49/288)*n^3 + (41/96)*n^2 + (2771/840)*n + 2.
%F Conjectures from _Colin Barker_, Sep 17 2018: (Start)
%F G.f.: x*(6 - 40*x + 127*x^2 - 224*x^3 + 255*x^4 - 177*x^5 + 77*x^6 - 19*x^7 + 2*x^8) / (1 - x)^9.
%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
%F (End)
%e Some solutions for n=4:
%e ..0..2..2..2....0..0..0..0....0..2..2..2....0..0..2..2....0..0..0..0
%e ..1..0..0..0....1..1..1..1....1..0..2..2....0..0..2..2....1..1..1..1
%e ..1..0..0..0....1..1..1..1....2..1..0..2....1..1..0..0....2..2..2..2
%e ..1..1..1..1....2..2..2..2....2..2..1..0....2..2..1..1....2..2..2..2
%Y Column 4 of A229445.
%K nonn
%O 1,1
%A _R. H. Hardin_, Sep 23 2013
| 