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 A277133 Number of distinct sets of periods of length >= ceiling(n/2) in all binary strings of length n. 1
 1, 2, 2, 4, 4, 7, 7, 11, 11, 17, 17, 25, 25, 35, 35, 48, 48, 65, 65, 86, 86, 113, 113, 143, 143, 180, 180, 227, 227, 284, 284, 346, 346, 421, 421, 508, 508, 610, 610, 726, 726, 861 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A period of a string x of length n is an integer p such that x[i] = x[i+p] for 1 <= i <= n-p. From Jeffrey Shallit, Jan 17 2019: (Start) Alternatively, the number of distinct sets of border lengths, restricted to at most n/2 in length, possible over all binary strings of length n. A border of a word is a nonempty prefix that is also a suffix. Alternatively, the number of distinct sets of lengths of palindromes that can begin a binary word of length n. (End) LINKS Table of n, a(n) for n=1..42. EXAMPLE For n = 5, the possible sets of periods of length >=3 are {5}, {3,5}, {4,5}, {3,4,5}, achieved by the strings 00001, 01001, 00010, 00100, respectively. CROSSREFS Cf. A005434, which is the sequence where there is no restriction on the size of the periods. Sequence in context: A099770 A099383 A341972 * A323539 A280954 A339244 Adjacent sequences: A277130 A277131 A277132 * A277134 A277135 A277136 KEYWORD nonn,more AUTHOR Jeffrey Shallit, Oct 01 2016 EXTENSIONS a(21)-a(42) from Lars Blomberg, Oct 08 2016 STATUS approved

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Last modified August 9 20:04 EDT 2024. Contains 375044 sequences. (Running on oeis4.)