OFFSET
0,2
COMMENTS
MATHEMATICA
Length/@NestList[DeleteCases[Flatten[Outer[Append, #, {0, 1}, 1], 1], {___, x__, x__, x__, x__, ___}] &, {{}}, 16]
PROG
(Python)
from itertools import product
def qf(s):
for l in range(1, len(s)//4 + 1):
for i in range(len(s) - 4*l + 1):
if s[i:i+l] == s[i+l:i+2*l] == s[i+2*l:i+3*l] == s[i+3*l:i+4*l]:
return False
return True
def a(n):
if n == 0: return 1
return 2*sum(1 for w in product("01", repeat=n-1) if qf("0"+"".join(w)))
print([a(n) for n in range(21)]) # Michael S. Branicky, Mar 14 2022
(Python) # faster, but > memory, version for initial segment of sequence
def iqf(s): # incrementally 4th-power free
for l in range(1, len(s)//4 + 1):
if s[-4*l:-3*l] == s[-3*l:-2*l] == s[-2*l:-l] == s[-l:]:
return False
return True
def aupton(nn, verbose=False):
alst, qfs = [1], set("0")
for n in range(1, nn+1):
an = 2*len(qfs)
qfsnew = set(q+i for q in qfs for i in "01" if iqf(q+i))
alst, qfs = alst+[an], qfsnew
if verbose: print(n, an)
return alst
print(aupton(20)) # Michael S. Branicky, Mar 14 2022
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Vladimir Reshetnikov, May 16 2016
EXTENSIONS
a(17)-a(30) from Lars Blomberg, Nov 11 2017
a(31)-a(34) from Michael S. Branicky, Mar 14 2022
STATUS
approved