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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 5 23:35 EDT 2024. Contains 374957 sequences. (Running on oeis4.)