A207148 - OEIS

%I #9 Jun 19 2018 12:35:50

%S 315,218,619,434,1238,866,2482,1730,4946,3458,9874,6914,19730,13826,

%T 39458,27650,78914,55298,157826,110594,315650,221186,631298,442370,

%U 1262594,884738,2525186,1769474,5050370,3538946,10100738,7077890

%N Number of (n+1) X 8 0..2 arrays with every 2 X 2 subblock having nonzero determinant and commuting with every horizontal or vertical neighbor.

%C Column 7 of A207149.

%H R. H. Hardin, <a href="/A207148/b207148.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) for n>14.

%F Empirical g.f.: x*(315 - 97*x - 229*x^2 + 9*x^3 + 2*x^4 - 2*x^5 + 8*x^6 - 8*x^7 - 16*x^8 + 16*x^9 - 16*x^10 + 16*x^11 - 16*x^12 + 16*x^13) / ((1 - x)*(1 - 2*x^2)). - _Colin Barker_, Jun 19 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A207149.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 15 2012