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%I #19 Oct 17 2016 06:55:36
%S 0,3,3,2,2,2,3,1,1,3,2,2,4,2,2,3,3,3,3,3,3,4,4,2,2,2,4,4,5,3,3,3,3,3,
%T 3,5,4,4,4,4,4,4,4,4,4,5,5,5,3,3,3,3,5,5,5,6,6,4,4,4,4,4,4,4,6,6,7,5,
%U 5,5,5,5,5,5,5,5,5,7,6,6,6,6,4,4,4,4,4,6,6,6,6,7,7,7,5,5,5,5,5,5,5,5,7,7,7
%N Array T read by diagonals: T(i,j)=least number of knight's moves on a chessboard (infinite in all directions) needed to move from (0,0) to (i,j).
%C For number of knight's moves to various subsets of the chessboard, see A018837, A183041 - A183053.
%F T(i,j) is given in cases:
%F Case 1: row 0
%F T(0,0)=0, T(1,0)=3, and for m>=1,
%F T(4m-2,0)=2m, T(4m-1,0)=2m+1, T(4m,0)=2m,
%F T(4m+1,0)=2m+1.
%F Case 2: row 1
%F T(0,1)=3, T(1,1)=2, and for m>=2,
%F T(4m-2,1)=2m-1, T(4m-1,1)=2m, T(4m,1)=2m+1,
%F T(4m+1,1)=2m+2.
%F Case 3: columns 1 and 2
%F (column 1) = (row 1); (column 2 = row 2).
%F Case 4: For i>=2 and j>=2,
%F T(i,j)=1+min{T(i-2,j-1),T(i-1,j-2)}.
%F Cases 1-4 determine T in the 1st quadrant;
%F all other T(i,j) are easily obtained by symmetry.
%e T(i,j) for -2<=i<=2 and -2<=j<=2:
%e 4 1 2 1 4=T(2,2)
%e 1 2 3 2 1=T(2,1)
%e 2 3 0 3 2=T(2,0)
%e 1 2 3 2 1=T(2,-1)
%e 4 1 2 1 4=T(2,-2)
%e Corner of the array, T(i,j) for i>=0, k>=0:
%e 0 3 2 3 2 3 4...
%e 3 2 1 2 3 4 3...
%e 2 1 4 3 2 3 4...
%e 3 2 3 2 3 4 2...
%Y Identical to A049604 except for T(1, 1).
%Y Cf. A183041,...,A183042.
%K nonn,tabl
%O 0,2
%A _Stewart Gordon_, Dec 05 2001
%E Formula, examples, and comments by _Clark Kimberling_, Dec 20 2010
%E Example corrected by _Clark Kimberling_, Oct 14 2016
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