A214944 Number of squarefree words of length 5 in an (n+1)-ary alphabet.

0, 30, 264, 1140, 3480, 8610, 18480, 35784, 64080, 107910, 172920, 265980, 395304, 570570, 803040, 1105680, 1493280, 1982574, 2592360, 3343620, 4259640, 5366130, 6691344, 8266200, 10124400, 12302550, 14840280, 17780364, 21168840, 25055130

Offset: 1

Author

R. H. Hardin, Jul 30 2012

Keywords

• nonn

Comments

Row 5 of A214943.

Examples

			Some solutions for n=2:
..1....2....2....0....1....0....0....0....2....1....2....2....0....2....1....2
..2....1....1....1....0....1....2....2....1....0....0....0....1....1....2....0
..0....0....2....2....2....2....1....0....0....2....1....1....0....2....0....2
..2....2....0....0....1....0....0....1....1....0....2....2....2....0....1....1
..1....1....2....2....2....1....2....0....2....1....0....1....0....1....0....0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

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

Conjectures from Colin Barker, Jul 22 2018: (Start)

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

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.

(End)