cp's OEIS Frontend

A233164 Number of n X 4 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, 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 A233164 #8 Oct 09 2018 14:39:53
%S A233164 11,64,1280,28672,720896,19922944,587202560,17985175552,562640715776,
%T A233164 17798344474624,566248488304640,18067175067615232,577305177233555456,
%U A233164 18460254872591663104,590511983140819435520,18892924695992401395712
%N A233164 Number of n X 4 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, 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 A233164 R. H. Hardin, <a href="/A233164/b233164.txt">Table of n, a(n) for n = 1..210</a>
%F A233164 Empirical: a(n) = 48*a(n-1) - 512*a(n-2) for n>3.
%F A233164 Conjectures from _Colin Barker_, Oct 09 2018: (Start)
%F A233164 G.f.: x*(11 - 464*x + 3840*x^2) / ((1 - 16*x)*(1 - 32*x)).
%F A233164 a(n) = 4^(2*n-3) * (2^n+12) for n>1.
%F A233164 (End)
%e A233164 Some solutions for n=4:
%e A233164 ..0..1..2..1....0..1..7..1....0..1..0..1....0..1..0..1....0..1..0..2
%e A233164 ..5..3..0..4....2..3..2..4....2..3..2..4....2..3..5..4....3..2..4..1
%e A233164 ..0..6..5..6....1..0..6..0....0..6..7..6....0..1..0..1....0..6..0..2
%e A233164 ..5..3..7..4....5..4..2..4....5..3..2..3....5..4..5..4....3..5..3..6
%Y A233164 Column 4 of A233168.
%K A233164 nonn
%O A233164 1,1
%A A233164 _R. H. Hardin_, Dec 05 2013