A207147 - OEIS

%I #9 Jun 19 2018 12:25:31

%S 122,187,218,374,434,754,866,1490,1730,2962,3458,5906,6914,11810,

%T 13826,23618,27650,47234,55298,94466,110594,188930,221186,377858,

%U 442370,755714,884738,1511426,1769474,3022850,3538946,6045698,7077890,12091394

%N Number of (n+1) X 7 0..2 arrays with every 2 X 2 subblock having nonzero determinant and commuting with every horizontal or vertical neighbor.

%C Column 6 of A207149.

%H R. H. Hardin, <a href="/A207147/b207147.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>13.

%F Empirical g.f.: x*(122 + 65*x - 213*x^2 + 26*x^3 - 2*x^4 + 8*x^5 - 8*x^6 - 16*x^7 + 16*x^8 - 16*x^9 + 16*x^10 - 16*x^11 + 16*x^12) / ((1 - x)*(1 - 2*x^2)). - _Colin Barker_, Jun 19 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A207149.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 15 2012