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A065775 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).

%I A065775 #30 Aug 20 2025 21:32:28
%S A065775 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 A065775 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 A065775 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 A065775 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).
%F A065775 From _Clark Kimberling_, Dec 20 2010: (Start)
%F A065775 T(i,j) is given in cases:
%F A065775 Case 1:  row 0
%F A065775   T(0,0)=0, T(1,0)=3, and for m>=1,
%F A065775   T(4m-2,0)=2m, T(4m-1,0)=2m+1, T(4m,0)=2m,
%F A065775   T(4m+1,0)=2m+1.
%F A065775 Case 2:  row 1
%F A065775   T(0,1)=3, T(1,1)=2, and for m>=1,
%F A065775   T(4m-2,1)=2m-1, T(4m-1,1)=2m, T(4m,1)=2m+1,
%F A065775   T(4m+1,1)=2m+2.
%F A065775 Case 3:  columns 0 and 1
%F A065775   (column 0 = row 0); (column 1 = row 1).
%F A065775 Case 4:  For i>=2 and j>=2,
%F A065775    T(i,j)=1+min{T(i-2,j-1),T(i-1,j-2)}.
%F A065775 Cases 1-4 determine T in the 1st quadrant;
%F A065775 all other T(i,j) are easily obtained by symmetry. (End)
%e A065775 From _Clark Kimberling_, Dec 20 2010: (Start)
%e A065775 T(i,j) for -2<=i<=2 and -2<=j<=2:
%e A065775   4 1 2 1 4=T(2,2)
%e A065775   1 2 3 2 1=T(2,1)
%e A065775   2 3 0 3 2=T(2,0)
%e A065775   1 2 3 2 1=T(2,-1)
%e A065775   4 1 2 1 4=T(2,-2)
%e A065775 Corner of the array, T(i,j) for i>=0, j>=0: [Corrected Oct 14 2016]
%e A065775   0 3 2 3 2 3 4...
%e A065775   3 2 1 2 3 4 3...
%e A065775   2 1 4 3 2 3 4...
%e A065775   3 2 3 2 3 4 2... (End)
%Y A065775 Identical to A049604 except for T(1, 1).
%Y A065775 For number of knight's moves to various subsets of the chessboard, see A018837, A183041-A183053.
%K A065775 nonn,tabl,changed
%O A065775 0,2
%A A065775 _Stewart Gordon_, Dec 05 2001