login
1/3 the number of n X 4 0..2 arrays with no element equal both to the element above and to the element to its left.
1

%I #11 Apr 14 2018 13:11:33

%S 27,1536,86688,4890528,275895264,15564399648,878052505824,

%T 49534593003552,2794452367733472,157646678048909856,

%U 8893504640414384352,501719578033435638816,28304087663951554461408,1596751280124982805188128

%N 1/3 the number of n X 4 0..2 arrays with no element equal both to the element above and to the element to its left.

%C Column 4 of A184694.

%H R. H. Hardin, <a href="/A184689/b184689.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 61*a(n-1) - 266*a(n-2) + 416*a(n-3) - 256*a(n-4).

%F Empirical g.f.: 3*x*(9 - 37*x + 58*x^2 - 32*x^3) / (1 - 61*x + 266*x^2 - 416*x^3 + 256*x^4). - _Colin Barker_, Apr 14 2018

%e Some solutions for 3 X 4 with a(1,1)=0:

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

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

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

%Y Cf. A184694.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 20 2011