A268905 - OEIS

%I #8 Jan 16 2019 15:03:36

%S 0,36,168,696,2664,9720,34344,118584,402408,1347192,4461480,14644152,

%T 47711592,154472184,497428776,1594323000,5089079016,16185567096,

%U 51311691432,162200044728,511395045480,1608569870328,5048863812648

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

%H R. H. Hardin, <a href="/A268905/b268905.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 9*a(n-2) for n>4.

%F Conjectures from _Colin Barker_, Jan 16 2019: (Start)

%F G.f.: 12*x^2*(3 - x)*(1 - x) / (1 - 3*x)^2.

%F a(n) = 8*3^(n-3) * (8*n-3) for n>2.

%F (End)

%e Some solutions for n=4:

%e ..0..2..1..2. .2..2..2..1. .0..0..2..1. .1..0..1..0. .1..1..0..1

%e ..2..2..2..2. .1..2..1..0. .0..1..0..0. .1..2..0..0. .0..1..2..2

%Y Row 2 of A268904.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 15 2016