Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the 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