|
%I #8 Nov 29 2018 03:00:54
%S 39,171,753,3333,14823,66219,297057,1337733,6045495,27408747,
%T 124625745,568146309,2596130823,11887635627,54533628609,250576195845,
%U 1153020767319,5312272049259,24501992068785,113120150702085,522688044131367
%N Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock summing to 2 4 or 6.
%H R. H. Hardin, <a href="/A251328/b251328.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 8*a(n-1) - 13*a(n-2) - 12*a(n-3).
%F Conjectures from _Colin Barker_, Nov 29 2018: (Start)
%F G.f.: 3*x*(13 - 47*x - 36*x^2) / ((1 - 4*x)*(1 - 4*x - 3*x^2)).
%F a(n) = (7*2^(3+2*n) + (35-13*sqrt(7))*(2-sqrt(7))^n + (2+sqrt(7))^n*(35+13*sqrt(7))) / 14.
%F (End)
%e Some solutions for n=4:
%e ..2..0....2..0....2..1....0..1....1..2....1..1....2..0....2..2....2..0....0..0
%e ..1..1....0..2....2..1....2..1....0..1....1..1....1..1....0..2....1..1....2..0
%e ..1..1....0..0....1..0....0..1....1..0....1..1....0..2....2..0....1..1....2..2
%e ..0..0....1..1....1..2....1..2....2..1....0..2....0..2....0..2....0..0....1..1
%e ..2..2....0..2....1..2....1..2....1..2....0..2....2..2....2..0....1..1....0..0
%Y Column 1 of A251335.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 01 2014
| 