A242468 - OEIS

%I #8 Nov 01 2018 11:38:50

%S 4,12,41,159,684,3204,16042,84412,460174,2570411,14593499,83749169,

%T 484000704,2809880001,16360962717,95445840289,557493277222,

%U 3258874744858,19059827706050,111510210083018,652534784892188,3819030330465099

%N Number of length n+2 0..5 arrays with no three equal elements in a row and new values 0..5 introduced in 0..5 order.

%H R. H. Hardin, <a href="/A242468/b242468.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 11*a(n-1) - 30*a(n-2) - 21*a(n-3) + 112*a(n-4) + 63*a(n-5) - 119*a(n-6) - 120*a(n-7) - 30*a(n-8).

%F Empirical g.f.: x*(4 - 32*x + 29*x^2 + 152*x^3 - 31*x^4 - 285*x^5 - 215*x^6 - 49*x^7) / ((1 - x - x^2)*(1 - 2*x - 2*x^2)*(1 - 3*x - 3*x^2)*(1 - 5*x - 5*x^2)). - _Colin Barker_, Nov 01 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Column 5 of A242472.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 15 2014