A229423 - OEIS

%I #8 Sep 15 2018 08:44:33

%S 8,27,83,222,524,1116,2187,4005,6936,11465,18219,27992,41772,60770,

%T 86451,120567,165192,222759,296099,388482,503660,645912,820091,

%U 1031673,1286808,1592373,1956027,2386268,2892492,3485054,4175331,4975787,5900040,6962931

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

%H R. H. Hardin, <a href="/A229423/b229423.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/360)*n^6 + (1/20)*n^5 + (5/18)*n^4 + (2/3)*n^3 + (799/360)*n^2 + (107/60)*n + 3.

%F Conjectures from _Colin Barker_, Sep 15 2018: (Start)

%F G.f.: x*(8 - 29*x + 62*x^2 - 72*x^3 + 48*x^4 - 18*x^5 + 3*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 ..1..0..0....1..1..0....0..0..0....1..1..1....1..0..0....0..0..0....1..0..0

%e ..2..1..1....2..1..0....1..1..0....1..1..1....2..1..1....1..1..0....2..1..0

%e ..2..1..1....2..2..1....1..1..1....1..1..1....2..2..1....1..1..0....2..1..1

%e ..2..2..1....2..2..1....1..1..1....1..1..1....2..2..2....1..1..1....2..2..2

%Y Column 3 of A229428.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 22 2013