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Number of n X 1 0..6 arrays with no element equal to another at a city block distance of exactly two, and new values 0..6 introduced in row major order.
1

%I #9 Aug 16 2018 08:58:49

%S 1,2,3,7,20,67,255,1079,4987,24759,129947,710791,4004619,23031191,

%T 134328379,790907943,4686298091,27884452663,166383085851,994632987335,

%U 5953222496203,35661292725975,213736364551163,1281494949329767

%N Number of n X 1 0..6 arrays with no element equal to another at a city block distance of exactly two, and new values 0..6 introduced in row major order.

%C Column 1 of A222779.

%H R. H. Hardin, <a href="/A222776/b222776.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 16*a(n-1) - 95*a(n-2) + 260*a(n-3) - 324*a(n-4) + 144*a(n-5) for n>7.

%F Empirical g.f.: x*(1 + x)*(1 - 15*x + 81*x^2 - 192*x^3 + 189*x^4 - 53*x^5) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 6*x)). - _Colin Barker_, Aug 16 2018

%e All solutions for n=3:

%e ..0....0....0

%e ..1....1....0

%e ..2....1....1

%Y Cf. A222779.

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 05 2013