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A323539
Number of distinct sets of lengths of squares that are prefixes of a length-n binary word.
1
1, 2, 2, 4, 4, 7, 7, 11, 11, 17, 17, 25, 25, 36, 36, 50, 50, 68, 68, 90, 90, 121, 121, 154, 154, 200, 200, 256, 256, 319, 319, 395, 395, 494, 494, 599, 599
OFFSET
1,2
COMMENTS
A square is a nonempty block of the form XX, where X is any block.
EXAMPLE
For n = 5, the possible sets are {2,4} (for 0000); {2} (for 0011); {4} (for 0101); and the empty set.
PROG
(C++) See Links section.
(Python)
from itertools import product
def a(n): return len(set(tuple(l for l in range(n//2) if w[l] == "0" and w[:l] == w[l+1:2*l+1]) for w in product("01", repeat=n-1)))
print([a(n) for n in range(1, 22)]) # Michael S. Branicky, Jul 23 2022
CROSSREFS
Similar to, but not the same as A277133.
Sequence in context: A099383 A341972 A277133 * A280954 A339244 A197122
KEYWORD
nonn,more
AUTHOR
Jeffrey Shallit, Jan 17 2019
EXTENSIONS
a(22)-a(37) from Rémy Sigrist, Jan 19 2019
STATUS
approved