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A229424 Number of n X 4 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing.

%I A229424 #8 Sep 15 2018 08:46:27
%S A229424 12,55,222,754,2204,5700,13345,28794,58053,110550,200533,348855,
%T A229424 585211,950897,1502166,2314261,3486210,5146473,7459536,10633552,
%U A229424 14929134,20669410,28251455,38159220,50978083,67411152,88297455,114632157
%N A229424 Number of n X 4 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing.
%H A229424 R. H. Hardin, <a href="/A229424/b229424.txt">Table of n, a(n) for n = 1..210</a>
%F A229424 Empirical: a(n) = (1/8064)*n^8 + (1/288)*n^7 + (103/2880)*n^6 + (17/90)*n^5 + (751/1152)*n^4 + (571/288)*n^3 + (7769/3360)*n^2 + (153/40)*n + 3.
%F A229424 Conjectures from _Colin Barker_, Sep 15 2018: (Start)
%F A229424 G.f.: x*(12 - 53*x + 159*x^2 - 272*x^3 + 302*x^4 - 222*x^5 + 103*x^6 - 27*x^7 + 3*x^8) / (1 - x)^9.
%F A229424 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 A229424 (End)
%e A229424 Some solutions for n=4:
%e A229424 ..2..2..1..0....1..1..0..0....2..1..0..0....1..1..1..0....1..0..0..0
%e A229424 ..2..2..2..1....2..1..0..0....2..2..1..1....2..1..1..0....2..1..0..0
%e A229424 ..2..2..2..1....2..1..1..1....2..2..1..1....2..2..1..0....2..1..1..1
%e A229424 ..2..2..2..1....2..2..2..2....2..2..2..2....2..2..2..1....2..1..1..1
%Y A229424 Column 4 of A229428.
%K A229424 nonn
%O A229424 1,1
%A A229424 _R. H. Hardin_, Sep 22 2013