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 A278299 a(n) is the tile count of the smallest polyomino with an n-coloring such that every color is adjacent to every other distinct color at least once. 0
 2, 4, 6, 9, 12, 15, 19, 24, 30, 34 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Only edge-to-edge adjacencies are considered. The sequence is bounded above by A053439(n-1). a(n) is bounded below by n * ceiling((n - 1)/4). This bound is achieved for n=2, n=6, and n=10. LINKS EXAMPLE Example: for n = 4, the following diagram gives a minimal polyomino of a(4) = 6 tiles:       +---+---+       | 1 | 4 |   +---+---+---+   | 4 | 3 | 2 |   +---+---+---+           | 1 |           +---+ Example: for n = 10, the following diagram gives a minimal polyomino of a(10) = 30 tiles. Note that redundant adjacencies, e.g., between 2 and 7, can exist in minimal diagrams.               +---+---+               | 8 | 6 |           +---+---+---+---+---+           | 3 | 2 | 5 | 9 | 4 |   +---+---+---+---+---+---+---+---+   | 2 | 7 | 5 | 1 | 4 | 2 | 10| 9 |   +---+---+---+---+---+---+---+---+   | 6 | 9 | 8 | 3 | 6 | 7 | 8 | 1 |   +---+---+---+---+---+---+---+---+   | 10| 3 | 4 | 7 | 1 | 10| 5 |   +---+---+---+---+---+---+---+ From Ryan Lee, May 14 2019: (Start) Example for n = 11:   +---+---+---+---+---+   | 9 | 11| 2 | 5 | 8 |   +---+---+---+---+---+---+   | 1 | 5 | 10| 9 | 2 | 1 |   +---+---+---+---+---+---+   | 4 | 6 | 11| 8 | 7 | 3 |   +---+---+---+---+---+---+   | 3 | 9 | 7 | 10| 6 | 2 |   +---+---+---+---+---+---+   | 11| 4 | 5 | 3 | 8 | 4 |   +---+---+---+---+---+---+   | 1 | 10|   | 6 | 1 | 7 |   +---+---+   +---+---+---+ (End) CROSSREFS Cf. A053439. Sequence in context: A194203 A261222 A130025 * A145802 A076271 A036441 Adjacent sequences:  A278296 A278297 A278298 * A278300 A278301 A278302 KEYWORD nonn,more AUTHOR Alec Jones and Peter Kagey, Nov 17 2016 EXTENSIONS a(11) from Ryan Lee, May 14 2019 STATUS approved

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Last modified September 18 10:13 EDT 2021. Contains 347518 sequences. (Running on oeis4.)