%I #7 Jan 29 2019 14:23:12

%S 8,1344,100800,6183744,345422784,18272616768,932758314432,

%T 46431146637120,2268408487407552,109231939785014592,

%U 5199659528294691264,245200862770851468096,11473103730476342109120,533310525557661056874816

%N Number of n X 2 0..7 arrays with some element plus some horizontally or vertically adjacent neighbor totalling seven exactly once.

%H R. H. Hardin, <a href="/A270112/b270112.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 86*a(n-1) - 1849*a(n-2) for n>3.

%F Conjectures from _Colin Barker_, Jan 29 2019: (Start)

%F G.f.: 8*x*(1 + 82*x + x^2) / (1 - 43*x)^2.

%F a(n) = 1344*43^(n-3) * (32*n-21) for n>1.

%F (End)

%e Some solutions for n=3:

%e ..0..1. .1..5. .4..5. .5..6. .2..5. .7..0. .2..0. .7..7. .4..0. .3..1

%e ..0..3. .5..4. .3..7. .1..4. .2..4. .4..6. .2..3. .2..0. .6..7. .4..5

%e ..7..5. .1..3. .0..3. .1..3. .1..2. .5..5. .5..0. .6..2. .6..5. .7..5

%Y Column 2 of A270118.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 11 2016