A221454 - OEIS

%I #7 Mar 14 2018 11:05:51

%S 0,1,2,7,24,88,328,1235,4668,17675,66974,253858,962352,3648397,

%T 13831870,52440191,198815196,753764564,2857736696,10834499599,

%U 41076702120,155733594211,590430871282,2238493367822,8486772670944,32175798041273

%N Number of 0..3 arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..3 order.

%C Column 3 of A221459.

%H R. H. Hardin, <a href="/A221454/b221454.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + a(n-2) - 6*a(n-3) - 3*a(n-4).

%F Empirical g.f.: x^2*(1 - 2*x - 2*x^2) / ((1 - x - x^2)*(1 - 3*x - 3*x^2)). - _Colin Barker_, Mar 14 2018

%e Some solutions for n=6:

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

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

%e ..1....2....2....1....0....2....2....2....1....2....2....2....2....2....2....2

%e ..0....2....3....2....1....0....1....3....2....1....1....1....3....2....3....0

%e ..0....1....2....2....2....1....3....3....1....2....2....0....3....0....1....0

%e ..1....3....1....0....0....3....1....2....2....3....0....3....1....3....2....1

%Y Cf. A221459.

%K nonn

%O 1,3

%A _R. H. Hardin_, Jan 17 2013