A214945 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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