cp's OEIS Frontend

A186474 Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

%I A186474 #8 Feb 28 2018 09:01:49
%S A186474 256,205,1098,1251,4895,5955,20079,27101,84228,123227,354915,553287,
%T A186474 1501107,2465976,6374253,10928793,27157017,48218637,116026140,
%U A186474 211997451,496891083,929460999,2132220387,4065922560,9164874045,17754363633
%N A186474 Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.
%C A186474 Column 1 of A186482.
%H A186474 R. H. Hardin, <a href="/A186474/b186474.txt">Table of n, a(n) for n = 1..200</a>
%F A186474 Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-4) - 3*a(n-5) for n>12.
%F A186474 Empirical g.f.: x*(256 - 307*x + 176*x^2 + 181*x^3 - 109*x^4 - 211*x^5 - 88*x^6 + 191*x^7 - 19*x^8 - 2*x^9 + 2*x^10 + 2*x^11) / ((1 - x)*(1 - x - 3*x^2 + 3*x^3 - 3*x^4)). - _Colin Barker_, Feb 28 2018
%e A186474 Some solutions for 3 X 2:
%e A186474 ..0..0....2..2....3..3....3..3....2..0....2..2....2..3....0..2....2..0....0..0
%e A186474 ..3..0....0..0....1..0....3..3....0..2....1..0....3..0....3..0....0..2....1..0
%e A186474 ..0..3....0..0....0..1....3..3....1..2....0..1....0..3....0..3....0..0....1..1
%Y A186474 Cf. A186482.
%K A186474 nonn
%O A186474 1,1
%A A186474 _R. H. Hardin_, Feb 22 2011