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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). 17
 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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For number of knight's moves to various subsets of the chessboard, see A018837, A183041 - A183053. LINKS FORMULA T(i,j) is given in cases: Case 1:  row 0   T(0,0)=0, T(1,0)=3, and for m>=1,   T(4m-2,0)=2m, T(4m-1,0)=2m+1, T(4m,0)=2m,   T(4m+1,0)=2m+1. Case 2:  row 1   T(0,1)=3, T(1,1)=2, and for m>=2,   T(4m-2,1)=2m-1, T(4m-1,1)=2m, T(4m,1)=2m+1,   T(4m+1,1)=2m+2. Case 3:  columns 1 and 2   (column 1) = (row 1); (column 2 = row 2). Case 4:  For i>=2 and j>=2,    T(i,j)=1+min{T(i-2,j-1),T(i-1,j-2)}. Cases 1-4 determine T in the 1st quadrant; all other T(i,j) are easily obtained by symmetry. EXAMPLE T(i,j) for -2<=i<=2 and -2<=j<=2: 4 1 2 1 4=T(2,2) 1 2 3 2 1=T(2,1) 2 3 0 3 2=T(2,0) 1 2 3 2 1=T(2,-1) 4 1 2 1 4=T(2,-2) Corner of the array, T(i,j) for i>=0, k>=0: 0 3 2 3 2 3 4... 3 2 1 2 3 4 3... 2 1 4 3 2 3 4... 3 2 3 2 3 4 2... CROSSREFS Identical to A049604 except for T(1, 1). Cf. A183041,...,A183042. Sequence in context: A064983 A124933 A133884 * A096837 A139092 A021305 Adjacent sequences:  A065772 A065773 A065774 * A065776 A065777 A065778 KEYWORD nonn,tabl AUTHOR Stewart Gordon, Dec 05 2001 EXTENSIONS Formula, examples, and comments by Clark Kimberling, Dec 20 2010 Example corrected by Clark Kimberling, Oct 14 2016 STATUS approved

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Last modified May 25 17:53 EDT 2020. Contains 334595 sequences. (Running on oeis4.)