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A279605
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Triangle T(n, k) read by rows: minimal number of knight moves to reach the central square on a (2*n+1) X (2*n+1) board starting from the k-th outermost square counted from middle of first rank for k = 1..n+1, or -1 if reaching the central square is impossible.
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1
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0, -1, -1, 4, 1, 2, 2, 3, 2, 3, 4, 3, 2, 3, 2, 4, 3, 4, 3, 4, 3, 4, 5, 4, 3, 4, 3, 4, 6, 5, 4, 5, 4, 5, 4, 5, 6, 5, 6, 5, 4, 5, 4, 5, 4, 6, 7, 6, 5, 6, 5, 6, 5, 6, 5, 8, 7, 6, 7, 6, 5, 6, 5, 6, 5, 6, 8, 7, 8, 7, 6, 7, 6, 7, 6, 7, 6, 7, 8, 9, 8, 7, 8, 7, 6, 7, 6, 7, 6, 7, 6
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OFFSET
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0,4
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LINKS
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FORMULA
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EXAMPLE
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Triangle starts
0;
-1, -1;
4, 1, 2;
2, 3, 2, 3;
4, 3, 2, 3, 2;
4, 3, 4, 3, 4, 3;
4, 5, 4, 3, 4, 3, 4;
6, 5, 4, 5, 4, 5, 4, 5;
6, 5, 6, 5, 4, 5, 4, 5, 4;
6, 7, 6, 5, 6, 5, 6, 5, 6, 5;
...
T(0, 1) = 0, because the board has just 1 square where the knight must start.
T(1, 1) and T(1, 2) = -1, because reaching the central square with a knight is not possible on a 3 X 3 board.
T(2, 1) = 4, because at least 4 moves are necessary on a 5 X 5 board to reach the central square when starting from a corner square.
T(2, 3) = 2 because 2 moves are necessary on a 5 X 5 board to reach the central square when starting from the middle of one side. - Andrew Howroyd, Feb 28 2020
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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a(5) corrected and terms a(15) and beyond from Andrew Howroyd, Feb 28 2020
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STATUS
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approved
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