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 A226595 Lengths of maximal nontouching increasing paths in n X n grids. 4
 0, 2, 4, 7, 9, 12, 15, 17, 20, 24, 27, 29, 33, 36, 39 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The path is not allowed to touch itself, not even on single points. "Increasing" means that the (Euclidean) length of each line segment must be strictly longer than the last. LINKS Giovanni Resta, Illustration of a(2)-a(9) Bert Dobbelaere, C++ program Gordon Hamilton, \$1,000,000 Unsolved Problem for Grade 8 (2011) Stan Wagon, Illustration for a(2)-a(12) FORMULA a(n) <= A226596(n) <= A160663(n-1). EXAMPLE An example for a(8)=17 ------------------------- 01 02  .  .  .  . 05  . ..  . 03  . 04  .  . 18 09 07  .  . 06  .  . 16 ..  .  .  .  .  .  . 14 ..  .  .  .  .  .  . 12 ..  . 08  .  .  .  .  . 10 17 15 13  .  .  .  . ..  .  .  . 11  .  .  . ------------------------- CROSSREFS Cf. A226596. Sequence in context: A184735 A184583 A189379 * A031435 A065560 A134886 Adjacent sequences:  A226592 A226593 A226594 * A226596 A226597 A226598 KEYWORD nonn,hard,nice,more AUTHOR Charles R Greathouse IV and Giovanni Resta, Jun 13 2013 EXTENSIONS a(10)-a(12) from Joseph DeVincentis via Charles R Greathouse IV, Oct 08 2015 a(13) from Charles R Greathouse IV, Oct 25 2015 using code from Joseph DeVincentis a(14)-a(15) from Bert Dobbelaere, Oct 05 2018 STATUS approved

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Last modified October 20 08:23 EDT 2019. Contains 328253 sequences. (Running on oeis4.)