A221540 - OEIS

%I #8 Oct 18 2017 18:23:16

%S 0,6,32,222,1455,9665,64047,424593,2814515,18656979,123673887,

%T 819813575,5434406883,36023773275,238795558499,1582935756291,

%U 10493015970771,69556445196155,461078023878243,3056408985571563,20260423189286435

%N Number of 0..6 arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.

%C Column 6 of A221542.

%H R. H. Hardin, <a href="/A221540/b221540.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) -4*a(n-2) +6*a(n-3) +26*a(n-4) +10*a(n-5) +16*a(n-6) +12*a(n-8).

%F Empirical g.f.: x^2*(6 - 10*x + 22*x^2 - 7*x^3 + 20*x^4 - 12*x^5 + 6*x^6) / (1 - 7*x + 4*x^2 - 6*x^3 - 26*x^4 - 10*x^5 - 16*x^6 - 12*x^8). - _Colin Barker_, Oct 18 2017

%e Some solutions for n=6

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

%e ..6....5....2....4....5....2....0....0....5....6....3....0....2....0....5....4

%e ..2....2....6....1....2....1....0....6....6....6....5....6....0....4....1....0

%e ..5....2....0....6....2....1....2....2....6....3....1....3....3....3....0....6

%e ..5....6....0....5....6....5....6....0....6....4....5....5....4....1....3....6

%e ..2....6....0....3....0....0....4....4....0....1....3....1....0....6....3....4

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 19 2013