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%I #37 Oct 06 2018 04:40:54
%S 0,2,4,7,9,12,15,17,20,24,27,29,33,36,39
%N Lengths of maximal nontouching increasing paths in n X n grids.
%C 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.
%H Giovanni Resta, <a href="/A226595/a226595.png">Illustration of a(2)-a(9)</a>
%H Bert Dobbelaere, <a href="/A226595/a226595.txt">C++ program</a>
%H Gordon Hamilton, <a href="https://www.youtube.com/watch?v=ZNmstUbD-pA">$1,000,000 Unsolved Problem for Grade 8</a> (2011)
%H Stan Wagon, <a href="/A226595/a226595_1.pdf">Illustration for a(2)-a(12)</a>
%F a(n) <= A226596(n) <= A160663(n-1).
%e An example for a(8)=17
%e -------------------------
%e 01 02 . . . . 05 .
%e .. . 03 . 04 . . 18
%e 09 07 . . 06 . . 16
%e .. . . . . . . 14
%e .. . . . . . . 12
%e .. . 08 . . . . .
%e 10 17 15 13 . . . .
%e .. . . . 11 . . .
%e -------------------------
%Y Cf. A226596.
%K nonn,hard,nice,more
%O 1,2
%A _Charles R Greathouse IV_ and _Giovanni Resta_, Jun 13 2013
%E a(10)-a(12) from Joseph DeVincentis via _Charles R Greathouse IV_, Oct 08 2015
%E a(13) from _Charles R Greathouse IV_, Oct 25 2015 using code from Joseph DeVincentis
%E a(14)-a(15) from _Bert Dobbelaere_, Oct 05 2018
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