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 A253620 Maximum number of segments in nonintersecting increasing path on n X n hexagonal (isogonal) grid. 1
 0, 3, 6, 10, 14, 19, 25, 30, 36 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The path cannot intersect itself, not even on single points. "Increasing" means that the (Euclidean) length of each segment must be strictly greater than that of the previous one. The analogous sequence for a triangular (isogonal) grid seems to satisfy a(n) = 2n+1, with 2^(n-2) such paths up to isomorphism. LINKS Tim Cieplowski, Illustration of first few terms Gordon Hamilton, \$1,000,000 Unsolved Problem for Grade 8 (2011) EXAMPLE An example for a(4) = 10        .   .   .   .     09   .   .   .   .   01   .   .   .   .   . 00  07   .   .   .   .  10   02  05   .   .   .  08      .   .   .   .  06       03   .   .  04 CROSSREFS Cf. A226595. Sequence in context: A310070 A036572 A139328 * A282731 A134919 A033437 Adjacent sequences:  A253617 A253618 A253619 * A253621 A253622 A253623 KEYWORD hard,more,nonn AUTHOR Tim Cieplowski, Jan 06 2015 STATUS approved

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Last modified March 21 01:18 EDT 2019. Contains 321356 sequences. (Running on oeis4.)