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A065775
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Array T read by diagonals: T(i,j)=least number of knight's moves on a chessboard infinite in all directions from (0,0) to (i,j).
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14
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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; internal format)
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OFFSET
| 0,2
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COMMENTS
| For number of knight's moves to various subsets of the chessboard, see A018837, A183041 - A183053.
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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.
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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 4 5...
3 2 1 2 3 4 3...
2 1 4 3 2 3 4...
3 2 3 2 3 4 2...
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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
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KEYWORD
| nonn,tabl
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AUTHOR
| Stewart Gordon (smjg(AT)iname.com), Dec 05 2001
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EXTENSIONS
| Formula, examples, and comments by Clark Kimberling (ck6(AT)evansville.edu), Dec 20 2010
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