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

1,2

Comments

Row 5 of A214943.

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)

Example

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

Crossrefs

Sequence in context: A230731 A053358 A163667 * A259455 A270852 A229427

Adjacent sequences: A214941 A214942 A214943 * A214945 A214946 A214947

Keyword

nonn

Author

R. H. Hardin, Jul 30 2012

Status

approved