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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.
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%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