OFFSET
0,2
COMMENTS
A border of a string w is a nonempty proper prefix of w that is also a suffix. The LB ("longest border") factorization of a string w is as follows: if w has no border, then the factorization is just (w). Otherwise, write w = (x)(w')(x) where x is the longest border of length <= |w|/2, and continue with w'. The length of the factorization is the number of factors. For example, 0101101010 = (010)(1)(10)(1)(010), and so has length 5.
LINKS
Michael S. Branicky, Table of n, a(n) for n = 0..41
PROG
(Python) # LBfactors() in A330882
from numba import njit
@njit() # comment out for n > 64
def a(n):
if n <= 1: return 2*n
LBfacsum = 0
for i in range(2**(n-1)): # only search 1st bit == 1 by symmetry
LBfacsum += LBfactors((1<<(n-1))|i, n)
return 2*LBfacsum # symmetry
print([a(n) for n in range(25)]) # Michael S. Branicky, Dec 31 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Apr 30 2020
EXTENSIONS
a(28)-a(35) from Bert Dobbelaere, May 12 2020
STATUS
approved