A082379 Number of length-n 7/3-power-free words over the alphabet {0,1}.

1, 2, 4, 6, 10, 14, 20, 24, 30, 40, 48, 56, 64, 76, 82, 92, 106, 124, 142, 152, 172, 192, 210, 220, 234, 256, 284, 308, 314, 332, 356, 372, 392, 420, 456, 488, 524, 560, 588, 608, 640, 684, 736, 764, 796, 832, 874, 892, 912, 948, 994, 1020, 1060, 1112, 1184

Offset

0,2

Links

Michael S. Branicky, Table of n, a(n) for n = 0..732

Juhani Karhumäki and Jeffrey Shallit, Polynomial versus exponential growth in repetition-free binary words, arXiv:math/0304095 [math.CO], April 7 2003.

Juhani Karhumäki and Jeffrey Shallit, Polynomial versus exponential growth in repetition-free binary words, Journal of Combinatorial Theory, Series A 105 (2004) 335-347.

Prog

(Python)
from fractions import Fraction
from functools import lru_cache
from itertools import count, islice, product
def period(x):
    for p in range(1, len(x)):
        if all(x[i] == x[i+p] for i in range(len(x)-p)):
            return p
    return len(x)
def exp(x):
    return Fraction(len(x), period(x))
@lru_cache(maxsize=None)
def cexp(x):
    if len(x) == 1: return 1
    return max(exp(x), cexp(x[:-1]), cexp(x[1:]))
def agen(): # generator of 7/3-power-free terms
    yield 1
    stfs = set("0")
    for n in count(1):
        yield 2*len(stfs)
        stfsnew = set(s+i for s in stfs for i in "01" if cexp(s+i) < Fraction(7, 3))
        stfs = stfsnew
print(list(islice(agen(), 60))) # Michael S. Branicky, Dec 08 2025

Crossrefs

Cf. A038952, A028445, A007777, A082380.

Sequence in context: A378195 A121386 A007777 * A167379 A213476 A277085

Adjacent sequences: A082376 A082377 A082378 * A082380 A082381 A082382

Keyword

nonn

Author

Ralf Stephan, Apr 10 2003

Extensions

Name changed by Jeffrey Shallit, Sep 26 2014

More terms from Jeffrey Shallit, Jul 17 2021

Status

approved