A214939 Number of squarefree words of length n in a 5-ary alphabet.

5, 20, 80, 300, 1140, 4260, 15960, 59580, 222600, 830880, 3102120, 11578800, 43220940, 161324400, 602159940, 2247585300, 8389237320, 31313155560, 116877700500, 436250537520

Offset: 1

Author

R. H. Hardin Jul 30 2012

Keywords

• nonn

Comments

All terms are multiples of 5 by symmetry. Michael S. Branicky, May 20 2021

Examples

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

Crossrefs

Column 4 of A214943.

Programs

Python

from itertools import product
def a(n):
  if n == 1: return 5
  squares = ["".join(u) + "".join(u)
    for r in range(1, n//2 + 1) for u in product("01234", repeat = r)]
  words = ("0"+"".join(w) for w in product("01234", repeat=n-1))
  return 5*sum(all(s not in w for s in squares) for w in words)
print([a(n) for n in range(1, 10)]) # Michael S. Branicky, May 20 2021