A188102 - OEIS

%I #8 Apr 26 2018 11:23:09

%S 13814,2374,3765,5661,8509,10229,10653,11245,12257,14405,17321,21217,

%T 28861,38625,49581,64510,84199,108156,136221,172155,220493,282863,

%U 360297,460529,592854,763168,976611,1248786,1601392,2054357,2627885,3360377

%N Number of (n+3) X 9 binary arrays with every 4 X 4 subblock commuting with each horizontal and vertical neighbor 4 X 4 subblock.

%C Column 6 of A188105.

%H R. H. Hardin, <a href="/A188102/b188102.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*a(n-5) + a(n-6) + a(n-8) - a(n-9) for n>16.

%F Empirical g.f.: x*(13814 - 25254*x + 12831*x^2 + 505*x^3 - 12862*x^4 + 24126*x^5 - 14127*x^6 - 337*x^7 - 14346*x^8 + 13704*x^9 + 673*x^10 - 1084*x^11 + 480*x^12 - 736*x^13 + 2401*x^15) / ((1 - x)*(1 - x - x^4 + x^5 - x^8)). - _Colin Barker_, Apr 26 2018

%e Some solutions for 5 X 9:

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

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

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

%e ..0..0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..0..0

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

%Y Cf. A188105.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 20 2011