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 A274020 Number of n-bead 5-ary necklaces (no turning over allowed) that avoid the subsequence 110. 3
 1, 5, 15, 44, 160, 604, 2510, 10545, 45825, 201669, 900307, 4057625, 18447565, 84444000, 388878560, 1799985435, 8368841895, 39062428790, 182961584260, 859612223990, 4049955449888, 19128675877279, 90553562670495, 429560546547595, 2041573370075675, 9719864998575489, 46350124359578975, 221352533355568044 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The pattern in this enumeration must be contiguous (all three values next to each other in one sequence of three letters). LINKS Table of n, a(n) for n=0..27. P. Hadjicostas and L. Zhang, On cyclic strings avoiding a pattern", Discrete Mathematics, 341 (2018), 1662-1674. Math Stackexchange, Marko Riedel et al., Counting circular sequences. Marko Riedel, Maple code for this sequence. FORMULA G.f.: 1 - Sum_{n>=1} (phi(n)/n)*log(x^(3*n)-q*x^n+1), where q=5 is the number of symbols in the alphabet we are using. - Petros Hadjicostas, Sep 12 2017 Define sequence (c(n): n>=1) by c(1) = q, c(2) = q^2, c(3) = q^3-3, and c(n) = q*c(n-1) - c(n-3) for n>=4. Then a(n) = (1/n)*Sum_{d|n} phi(n/d)*c(d) for n>=1. (Here q=5.) - Petros Hadjicostas, Jan 29 2018 EXAMPLE The following necklace: . 1-1 . / \ . 0 0 . | | . 1 3 . \ / . 2-4 contains one instance of the subsequence starting in the upper left corner. Unlike a bracelet, the necklace is oriented. CROSSREFS Cf. A000031, A274017, A274018, A274019. Sequence in context: A064453 A059251 A295179 * A109952 A146632 A076103 Adjacent sequences: A274017 A274018 A274019 * A274021 A274022 A274023 KEYWORD nonn AUTHOR Marko Riedel, Jun 06 2016 STATUS approved

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Last modified September 19 12:50 EDT 2024. Contains 376012 sequences. (Running on oeis4.)