%I #9 Jul 22 2018 08:44:37

%S 0,30,264,1140,3480,8610,18480,35784,64080,107910,172920,265980,

%T 395304,570570,803040,1105680,1493280,1982574,2592360,3343620,4259640,

%U 5366130,6691344,8266200,10124400,12302550,14840280,17780364,21168840,25055130

%N Number of squarefree words of length 5 in an (n+1)-ary alphabet.

%C Row 5 of A214943.

%H R. H. Hardin, <a href="/A214944/b214944.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^5 + n^4 - 2*n^3 - n^2 + n.

%F Conjectures from _Colin Barker_, Jul 22 2018: (Start)

%F G.f.: 6*x^2*(5 + 14*x + x^2) / (1 - x)^6.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

%F (End)

%e Some solutions for n=2:

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

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_, Jul 30 2012