This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A208716 #16 Aug 22 2024 17:15:08 %S A208716 3,5,7,12,18,34,56,111,207,427,859,1851,3930,8672,19092,42845,96243, %T A208716 218567,497183,1138084,2610226,6009662,13861968,32057868,74260243, %U A208716 172351415,400589343,932486879,2173368730,5071877864,11849063220,27711739481 %N A208716 Number of n-bead necklaces labeled with numbers 1..3 allowing reversal, with no adjacent beads differing by more than 1. %H A208716 Andrew Howroyd, <a href="/A208716/b208716.txt">Table of n, a(n) for n = 1..100</a> %H A208716 Stephan Mertens, <a href="https://arxiv.org/abs/2408.08053">Domination Polynomials of the Grid, the Cylinder, the Torus, and the King Graph</a>, arXiv:2408.08053 [math.CO], 2024. See p. 22. %F A208716 a(2n+1) = (1/2) * (A208772(2n+1) + A078057(n+1)). - _Andrew Howroyd_, Mar 03 2017 %F A208716 a(2n) = (1/2) * A208772(2n) + (1/4) * (A078057(n) + A078057(n+1)). - _Andrew Howroyd_, Mar 03 2017 %e A208716 All solutions for n=4: %e A208716 ..2....1....1....2....2....1....2....1....1....1....3....2 %e A208716 ..2....2....1....3....3....1....2....2....2....1....3....2 %e A208716 ..2....3....1....3....2....2....3....1....2....1....3....2 %e A208716 ..3....2....2....3....3....2....3....2....2....1....3....2 %Y A208716 Column 3 of A208721. %Y A208716 Cf. A208772, A078057. %K A208716 nonn %O A208716 1,1 %A A208716 _R. H. Hardin_, Mar 01 2012