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%I #12 Aug 13 2018 09:12:04
%S 0,1,0,2,1,0,1,2,1,0,2,3,2,1,0,1,2,3,2,1,0,2,3,4,3,2,1,0,1,2,3,2,3,2,
%T 1,0,2,1,2,3,4,3,2,1,0,3,2,3,4,5,4,3,2,1,0,2,1,2,3,4,3,4,3,2,1,0,3,2,
%U 1,2,3
%N Triangle T read by rows: T(n,k) equals the Manhattan distance between n and k when integers are arranged in a spiral.
%C Spiral begins (0 at the center):
%C .
%C 42--43--44--45--46--47--48
%C |
%C 41 20--21--22--23--24--25
%C | | |
%C 40 19 6---7---8---9 26
%C | | | | |
%C 39 18 5 0---1 10 27
%C | | | | | |
%C 38 17 4---3---2 11 28
%C | | | |
%C 37 16--15--14--13--12 29
%C | |
%C 36--35--34--33--32--31--30
%F T(n,n) = 0, T(n+1,n) = 1, T(n+2,n) = 2, T(n,k) <= n-k.
%e Triangle begins, 0 <= k <= n:
%e 0
%e 1, 0
%e 2, 1, 0
%e 1, 2, 1, 0
%e 2, 3, 2, 1, 0
%e 1, 2, 3, 2, 1, 0
%e 2, 3, 4, 3, 2, 1, 0
%e 1, 2, 3, 2, 3, 2, 1, 0
%e 2, 1, 2, 3, 4, 3, 2, 1, 0
%e 3, 2, 3, 4, 5, 4, 3, 2, 1, 0
%e 2, 1, 2, 3, 4, 3, 4, 3, 2, 1, 0
%e 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0
%e 4, 3, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0
%e 3, 2, 1, 2, 3, 4, 5, 4, 3, 4, 3, 2, 1, 0
%e 2, 3, 2, 1, 2, 3, 4, 3, 4, 5, 4, 3, 2, 1, 0
%e 3, 4, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0
%K nonn,tabl
%O 0,4
%A _Philippe Deléham_, Mar 11 2013
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