login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Number of (n+2) X 3 binary arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock.
1

%I #8 May 03 2018 07:02:48

%S 512,112,228,415,616,880,1205,1508,2008,2793,3776,5220,7274,9829,

%T 13345,18256,24651,33451,45700,61988,84197,114766,155769,211493,

%U 287826,390881,530866,722029,980917,1332459,1811512,2461345,3343817,4544963,6175777

%N Number of (n+2) X 3 binary arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock.

%C Column 1 of A190033.

%H R. H. Hardin, <a href="/A190025/b190025.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5) +a(n-6) -a(n-7) for n>11.

%F Empirical g.f.: x*(512 - 912*x + 516*x^2 - 441*x^3 + 926*x^4 - 453*x^5 - 522*x^6 + 364*x^7 + 18*x^8 + 37*x^9 + 19*x^10) / ((1 - x)*(1 - x - x^3 + x^4 - x^6)). - _Colin Barker_, May 03 2018

%e Some solutions for 4 X 3:

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

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

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

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

%Y Cf. A190033.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 04 2011