A214946 Number of squarefree words of length 7 in an (n+1)-ary alphabet.

0, 60, 1848, 15960, 80040, 292740, 868560, 2218608, 5062320, 10575180, 20577480, 37769160, 66015768, 110690580, 179077920, 280842720, 428571360, 638388828, 930657240, 1330760760, 1869981960, 2586474660, 3526338288, 4744798800

Offset

1,2

Comments

Row 7 of A214943.

Links

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

Formula

Empirical: a(n) = n^7 + n^6 - 4*n^5 - 3*n^4 + 5*n^3 + 2*n^2 - 2*n.

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

G.f.: 12*x^2*(5 + 114*x + 238*x^2 + 62*x^3 + x^4) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

Example

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

Crossrefs

Cf. A214943.

Sequence in context: A035725 A035800 A017723 * A058836 A166792 A013925

Adjacent sequences: A214943 A214944 A214945 * A214947 A214948 A214949

Keyword

nonn

Author

R. H. Hardin, Jul 30 2012

Status

approved