%I #22 Apr 17 2021 01:45:56

%S 1,4,16,60,228,864,3264,12336,46632,176208,665892,2516412,9509364,

%T 35935476,135798588,513176076,1939267560,7328398344

%N Number of quaternary cubefree words of length n.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CubefreeWord.html">Cubefree Word.</a>

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

%o (Python)

%o from itertools import product

%o def cf(s):

%o for l in range(1, len(s)//3+1):

%o for i in range(len(s) - 3*l+1):

%o if s[i:i+l]*2 == s[i+l:i+3*l]: return False

%o return True

%o def a(n):

%o if n == 0: return 1

%o return 4*sum(cf("0"+"".join(w)) for w in product("0123", repeat=n-1))

%o print([a(n) for n in range(1, 12)]) # _Michael S. Branicky_, Apr 16 2021

%Y Cf. A028445, A051042.

%K nonn,more

%O 0,2

%A _Eric W. Weisstein_

%E More terms from _Sascha Kurz_, Mar 22 2002

%E a(0) prepended and a(16)-a(17) from _Michael S. Branicky_, Apr 16 2021