A183615 - OEIS

%I #13 Jul 22 2013 14:50:56

%S 6,56,528,4992,47232,446976,4230144,40034304,378888192,3585835008,

%T 33936703488,321180401664,3039683936256,28767877595136,

%U 272262116671488,2576716337774592,24386305253179392,230794470931562496

%N 1/120 the number of (n+1) X 3 0..4 arrays with every 2 X 2 subblock containing four distinct values.

%C Column 2 of A183622.

%H R. H. Hardin, <a href="/A183615/b183615.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 12*a(n-1)-24*a(n-2).

%F Conjecture: G.f.: 1/(x*(3- G(0))) -1/x, where G(k)= 1 + 2^k/(1 - 2*x/(2*x + 2^k*1/G(k+1) )); (continued fraction). - _Sergei N. Gladkovskii_, Jul 21 2013

%e Some solutions with the first square being 0123 for 5 X 3

%e ..0..1..0....0..1..2....0..1..2....0..1..4....0..1..4....0..1..4....0..1..4

%e ..2..3..2....2..3..0....2..3..0....2..3..2....2..3..2....2..3..2....2..3..2

%e ..0..4..0....0..4..2....0..1..2....4..1..4....0..1..0....1..0..1....4..1..4

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

%e ..2..0..4....0..2..1....0..1..2....4..1..2....0..1..2....1..0..2....1..4..1

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 06 2011