A221457 - OEIS

%I #7 Aug 05 2018 08:32:44

%S 0,1,2,7,25,102,456,2218,11605,64647,379349,2320555,14658240,94843284,

%T 624544847,4164947151,28025750099,189783308469,1290899153376,

%U 8808076870934,60230644078721,412493027114619,2827998455493193

%N Number of 0..6 arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..6 order.

%C Column 6 of A221459.

%H R. H. Hardin, <a href="/A221457/b221457.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 16*a(n-1) - 79*a(n-2) + 70*a(n-3) + 361*a(n-4) - 372*a(n-5) - 964*a(n-6) + 144*a(n-7) + 1116*a(n-8) + 720*a(n-9) + 144*a(n-10).

%F Empirical g.f.: x^2*(1 - 14*x + 54*x^2 + x^3 - 246*x^4 - 41*x^5 + 411*x^6 + 364*x^7 + 91*x^8) / ((1 - x - x^2)*(1 - 2*x - 2*x^2)*(1 - 3*x - 3*x^2)*(1 - 4*x - 4*x^2)*(1 - 6*x - 6*x^2)). - _Colin Barker_, Aug 05 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 ..2....2....2....2....2....2....1....2....1....2....2....0....2....0....2....2

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

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

%e ..1....2....3....2....0....4....3....1....1....1....3....1....1....4....4....1

%Y Cf. A221459.

%K nonn

%O 1,3

%A _R. H. Hardin_, Jan 17 2013