|
%I #9 Jun 15 2018 11:01:40
%S 96,181,232,534,686,1589,2042,4751,6110,14239,18318,42705,54942,
%T 128103,164814,384297,494430,1152879,1483278,3458625,4449822,10375863,
%U 13349454,31127577,40048350,93382719,120145038,280148145,360435102,840444423
%N Number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock having nonzero determinant and commuting with every horizontal or vertical neighbor.
%C Column 2 of A206343.
%H R. H. Hardin, <a href="/A206337/b206337.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) for n>11.
%F Empirical g.f.: x*(96 + 85*x - 237*x^2 + 47*x^3 - x^4 - 3*x^5 - 3*x^6 + 2*x^9 + 2*x^10) / ((1 - x)*(1 - 3*x^2)). - _Colin Barker_, Jun 15 2018
%e Some solutions for n=4:
%e ..3..0..1....0..1..0....1..3..1....0..2..0....0..1..0....1..0..1....0..1..0
%e ..0..3..0....3..0..1....3..1..3....3..0..2....1..0..1....0..1..0....3..0..1
%e ..2..0..3....0..3..0....1..3..1....0..3..0....0..1..0....2..0..1....0..3..0
%e ..0..2..0....1..0..3....3..1..3....1..0..3....2..0..1....0..2..0....3..0..3
%e ..1..0..2....0..1..0....1..3..1....0..1..3....0..2..1....1..0..2....0..3..3
%Y Cf. A206343.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 06 2012
| 