A051043 Number of quaternary cubefree words of length n.

1, 4, 16, 60, 228, 864, 3264, 12336, 46632, 176208, 665892, 2516412, 9509364, 35935476, 135798588, 513176076, 1939267560, 7328398344

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Eric Weisstein's World of Mathematics, Cubefree Word.

Example

a(3) counts the 64 three-letter words minus 000, 111, 222, and 333.

Prog

(Python)
from itertools import product
def cf(s):
  for l in range(1, len(s)//3+1):
    for i in range(len(s) - 3*l+1):
      if s[i:i+l]*2 == s[i+l:i+3*l]: return False
  return True
def a(n):
  if n == 0: return 1
  return 4*sum(cf("0"+"".join(w)) for w in product("0123", repeat=n-1))
print([a(n) for n in range(1, 12)]) # Michael S. Branicky, Apr 16 2021

Crossrefs

Cf. A028445, A051042.

Sequence in context: A032106 A269462 A047097 * A123620 A234008 A355351

Adjacent sequences: A051040 A051041 A051042 * A051044 A051045 A051046

Keyword

nonn,more

Author

Eric W. Weisstein

Extensions

More terms from Sascha Kurz, Mar 22 2002

a(0) prepended and a(16)-a(17) from Michael S. Branicky, Apr 16 2021

Status

approved