%I
%S 36,216,2166,18384,146064,1114848,8277072,60218112,431354928,
%T 3052215072,21383561232,148585984320,1025363155440,7034327057760,
%U 48013557090768,326276117933952,2208609401649072,14899002865010592,100198549907000208
%N Number of n X 4 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.
%H R. H. Hardin, <a href="/A269031/b269031.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 14*a(n1)  57*a(n2) + 56*a(n3)  16*a(n4) for n>5.
%F Empirical g.f.: 6*x*(6  48*x + 199*x^2  274*x^3 + 105*x^4) / (1  7*x + 4*x^2)^2.  _Colin Barker_, Jan 18 2019
%e Some solutions for n=4:
%e ..0..0..0..1. .1..0..0..1. .0..1..2..1. .2..1..0..0. .2..2..1..2
%e ..0..1..0..1. .1..0..0..0. .2..1..0..1. .2..1..0..1. .2..2..2..1
%e ..2..1..2..2. .0..0..1..0. .0..1..0..1. .2..1..0..1. .2..1..2..2
%e ..2..1..2..2. .0..1..0..0. .2..1..2..0. .2..1..2..2. .2..1..2..2
%Y Column 4 of A269035.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 18 2016
