A230726 - OEIS

%I #9 Sep 22 2018 11:50:59

%S 0,2,30,396,6212,95412,1459082,22379112,343179162,5262047702,

%T 80687972676,1237264461260,18972099054156,290916616713522,

%U 4460891769710192,68402949461361234,1048885241311782830,16083520658051806236

%N Number of n X 4 0..5 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 6, and upper left element zero.

%H R. H. Hardin, <a href="/A230726/b230726.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 16*a(n-1) - 12*a(n-2) + 87*a(n-3) - 918*a(n-4) + 61*a(n-5) - a(n-6).

%F Empirical g.f.: 2*x^2*(1 - x)*(1 - 30*x^2 + x^3) / (1 - 16*x + 12*x^2 - 87*x^3 + 918*x^4 - 61*x^5 + x^6). - _Colin Barker_, Sep 22 2018

%e Some solutions for n=4:

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

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

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

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

%Y Column 4 of A230730.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 28 2013