A183357 - OEIS

%I #9 Mar 28 2018 08:14:18

%S 108,2304,3888,9216,24192,57600,137088,331776,802944,1937664,4675968,

%T 11289600,27257472,65804544,158864256,383533056,925932672,2235398400,

%U 5396727168,13028852736,31454434944,75937722624,183329877888

%N One quarter the number of n X 5 1..4 arrays with no two neighbors of any element equal to each other.

%C Column 5 of A183362.

%H R. H. Hardin, <a href="/A183357/b183357.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) + 2*a(n-3) + a(n-4) for n>7.

%F Empirical g.f.: 36*x*(3 + 58*x - 20*x^2 + 34*x^3 + 29*x^4 - 24*x^5 - 12*x^6) / ((1 + x^2)*(1 - 2*x - x^2)). - _Colin Barker_, Mar 28 2018

%e Some solutions for 7 X 5 with a(1,1)=1:

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

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

%e ..2..2..1..1..3....2..3..3..1..2....2..1..3..2..2....3..3..1..1..2

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

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

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

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

%Y Cf. A183362.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 04 2011