A323539 Number of distinct sets of lengths of squares that are prefixes of a length-n binary word.

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.

Links

Table of n, a(n) for n=1..37.

Rémy Sigrist, C++ program

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

Adjacent sequences: A323536 A323537 A323538 * A323540 A323541 A323542

Keyword

nonn,more

Author

Jeffrey Shallit, Jan 17 2019

Extensions

a(22)-a(37) from Rémy Sigrist, Jan 19 2019

Status

approved