A214945 Number of squarefree words of length 6 in an (n+1)-ary alphabet.

0, 42, 696, 4260, 16680, 50190, 126672, 281736, 569520, 1068210, 1886280, 3169452, 5108376, 7947030, 11991840, 17621520, 25297632, 35575866, 49118040, 66704820, 89249160, 117810462, 153609456, 198043800, 252704400, 319392450, 400137192

Offset

1,2

Comments

Row 6 of A214943.

Links

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

Formula

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

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

G.f.: 6*x^2*(7 + 67*x + 45*x^2 + x^3) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

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

Crossrefs

Cf. A214943.

Sequence in context: A269659 A007746 A200853 * A159947 A330845 A333113

Adjacent sequences: A214942 A214943 A214944 * A214946 A214947 A214948

Keyword

nonn

Author

R. H. Hardin, Jul 30 2012

Status

approved