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 A350362 2-tone chromatic number of an n-cycle. 3
 6, 6, 5, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS The 2-tone chromatic number of a graph G is the smallest number of colors for which G has a coloring where every vertex has two distinct colors, no adjacent vertices have a common color, and no pair of vertices at distance 2 have two common colors. There is no 2-tone 5-coloring for cycles of length 3, 4, or 7 since the Petersen graph does not contain cycles of these lengths. LINKS Allan Bickle and B. Phillips, t-Tone Colorings of Graphs, Utilitas Math, 106 (2018) 85-102. Allan Bickle, 2-Tone coloring of joins and products of graphs, Congr. Numer. 217 (2013), 171-190. N. Fonger, J. Goss, B. Phillips, and C. Segroves, Math 6450: Final Report, Group #2 Study Project, 2009. Index entries for linear recurrences with constant coefficients, signature (1). FORMULA a(n) = 5 for all n>7. G.f.: x^3*(1 + x + x^4) + 5*x^3/(1 - x). - Stefano Spezia, Dec 27 2021 EXAMPLE The colorings for (broken) cycles with orders 3 through 9 are shown below. -12-34-56- -12-34-15-36- -12-34-51-23-45- -12-34-15-32-14-35- -12-34-56-13-24-35-46- -12-34-15-23-14-25-13-45- -12-34-15-32-14-25-13-24-35- Colorings for larger cycles can be spliced together from broken cycles of lengths 5, 6, and 8. CROSSREFS Cf. A350361. Sequence in context: A197478 A260713 A101801 * A351120 A199664 A019180 Adjacent sequences: A350359 A350360 A350361 * A350363 A350364 A350365 KEYWORD nonn,easy AUTHOR Allan Bickle, Dec 26 2021 STATUS approved

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Last modified November 30 05:38 EST 2022. Contains 358431 sequences. (Running on oeis4.)