A233198 - OEIS

A233198

Number of n X 4 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).

%I #7 Oct 10 2018 08:36:09

%S 11,528,62720,7802880,981532672,123833679872,15635845218304,

%T 1974688792182784,249403601212932096,31500304517060100096,

%U 3978590250109478371328,502509651344957204594688

%N Number of n X 4 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).

%H R. H. Hardin, <a href="/A233198/b233198.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 208*a(n-1) - 13312*a(n-2) + 442368*a(n-3) - 8650752*a(n-4) + 67108864*a(n-5) for n>6.

%F Empirical g.f.: x*(11 - 1760*x + 99328*x^2 - 3080192*x^3 + 55050240*x^4 - 369098752*x^5) / ((1 - 16*x)*(1 - 192*x + 10240*x^2 - 278528*x^3 + 4194304*x^4)). - _Colin Barker_, Oct 10 2018

%e Some solutions for n=3:

%e ..0..1..2..0....0..1..2..6....0..1..2..3....0..1..2..3....0..1..0..2

%e ..2..0..3..5....3..0..4..5....2..0..6..2....2..3..6..5....3..2..1..4

%e ..6..5..1..7....1..2..1..4....1..5..7..3....6..5..3..0....6..3..5..6

%Y Column 4 of A233202.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 05 2013