A221588 - OEIS

%I #8 Aug 09 2018 08:56:08

%S 4,40,418,3760,31416,256736,2075520,16690688,133871616,1072357376,

%T 8584396800,68697325568,549667209216,4397692092416,35182954414080,

%U 281469306011648,2251777130889216,18014307778297856,144114825151119360

%N Equals one maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to exactly one of their king-move neighbors in a random 0..3 n X 3 array.

%C Column 3 of A221590.

%H R. H. Hardin, <a href="/A221588/b221588.txt">Table of n, a(n) for n = 1..174</a>

%F Empirical: a(n) = 12*a(n-1) -32*a(n-2) for n>6.

%F Conjectures from _Colin Barker_, Aug 09 2018: (Start)

%F G.f.: 2*x*(2 - 4*x + 33*x^2 + 12*x^3 - 164*x^4 + 32*x^5) / ((1 - 4*x)*(1 - 8*x)).

%F a(n) = 8^n - 169*2^(2*n-7) for n>4.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A221590.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 20 2013