A186461 - OEIS

%I #9 Apr 18 2018 06:25:39

%S 359,457,846,1493,2285,3677,5633,9477,13245,20281,27573,43177,62025,

%T 98157,144825,224381,333321,511281,765293,1167881,1755461,2669577,

%U 4022697,6104941,9213769,13965837,21097609,31954865,48300653,73123993

%N Number of (n+1) X 9 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

%C Column 8 of A186462.

%H R. H. Hardin, <a href="/A186461/b186461.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-4) - a(n-5) for n>14.

%F Empirical g.f.: x*(359 - 261*x - 68*x^2 + 519*x^3 - 505*x^4 + 244*x^5 + 30*x^6 + 641*x^7 - 1432*x^8 - 12*x^9 - 1624*x^10 + 1200*x^11 - 780*x^12 + 1936*x^13) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - _Colin Barker_, Apr 18 2018

%e Some solutions for 3 X 9:

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

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

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

%Y Cf. A186462.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 22 2011