A214940 Number of squarefree words of length n in a 6-ary alphabet

6, 30, 150, 720, 3480, 16680, 80040, 383520, 1838160, 8807400, 42202560, 202209720, 968880960, 4642304520, 22243228680, 106576361760, 510651000360

Offset

1,1

Comments

Column 5 of A214943

Links

Table of n, a(n) for n=1..17.

Example

Some solutions for n=6
..4....4....4....1....5....5....4....5....2....1....5....4....2....1....4....5
..0....5....5....4....2....4....1....1....1....3....3....1....4....2....1....2
..5....3....0....5....3....2....4....4....0....1....4....0....3....0....2....1
..3....4....3....3....2....5....2....5....5....4....0....3....5....4....4....0
..5....1....4....5....1....3....3....3....2....5....3....4....0....2....5....5
..0....0....5....2....3....4....2....5....3....2....4....2....2....4....1....1

Prog

(Python)
from itertools import product
def a(n):
    if n == 1: return 6
    squares = ["".join(u) + "".join(u)
        for r in range(1, n//2 + 1) for u in product("012345", repeat=r)]
    words = ("0"+"".join(w) for w in product("012345", repeat=n-1))
    return 6*sum(all(s not in w for s in squares) for w in words)
print([a(n) for n in range(1, 9)]) # Michael S. Branicky, Jun 30 2021

Crossrefs

Sequence in context: A079738 A127741 A073965 * A002913 A157519 A075886

Adjacent sequences: A214937 A214938 A214939 * A214941 A214942 A214943

Keyword

nonn

Author

R. H. Hardin Jul 30 2012

Status

approved