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

Author

R. H. Hardin, Jul 30 2012

Keywords

• nonn

Comments

Row 6 of A214943.

Examples

			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
		

Links

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

Crossrefs

Cf. A214943.

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)