%I #12 Aug 16 2018 13:23:13
%S 1,2,3,7,20,66,238,902,3510,13846,54998,219222,875350,3498326,
%T 13987158,55936342,223720790,894834006,3579237718,14316754262,
%U 57266623830,229065708886,916261262678,3665041904982,14660161328470,58640632730966
%N Number of n X 1 0..4 arrays with no element equal to another at a city block distance of exactly two, and new values 0..4 introduced in row major order.
%C Column 1 of A222944.
%H R. H. Hardin, <a href="/A222939/b222939.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3) for n>5.
%F Conjectures from _Colin Barker_, Aug 16 2018: (Start)
%F G.f.: x*(1 + x)*(1 - 6*x + 9*x^2 - 3*x^3) / ((1 - x)*(1 - 2*x)*(1 - 4*x)).
%F a(n) = (256 + 9*2^(3+n) + 5*4^n) / 384 for n>2.
%F (End)
%e All solutions for n=3:
%e ..0....0....0
%e ..0....1....1
%e ..1....2....1
%Y Cf. A222944.
%K nonn
%O 1,2
%A _R. H. Hardin_, Mar 09 2013