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%I #8 Aug 16 2018 08:59:10
%S 7,96,216,600,1536,4056,10584,27744,72600,190104,497664,1302936,
%T 3411096,8930400,23380056,61209816,160249344,419538264,1098365400,
%U 2875557984,7528308504,19709367576,51599794176,135090015000,353670250776
%N Number of n X 4 0..3 arrays with no element equal to another at a city block distance of exactly two, and new values 0..3 introduced in row major order.
%C Column 4 of A222838.
%H R. H. Hardin, <a href="/A222834/b222834.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - a(n-3) for n>4.
%F Conjectures from _Colin Barker_, Aug 16 2018: (Start)
%F G.f.: x*(7 + 82*x + 10*x^2 - 17*x^3) / ((1 + x)*(1 - 3*x + x^2)).
%F a(n) = (3/5)*2^(2-n)*((-1)^n*2^(2+n) + (3-sqrt(5))^(1+n) + (3+sqrt(5))^(1+n)) for n>1.
%F (End)
%e Some solutions for n=4:
%e ..0..0..1..1....0..1..2..3....0..1..1..2....0..1..1..2....0..0..1..2
%e ..2..2..3..3....2..1..0..3....2..2..0..3....0..2..3..3....3..2..1..3
%e ..3..1..0..2....2..3..0..1....1..3..0..1....3..2..0..1....1..2..0..3
%e ..3..1..0..2....0..3..2..2....0..3..2..1....3..1..0..2....1..3..0..1
%Y Cf. A222838.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 06 2013
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