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A279605
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.
1
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
OFFSET
0,4
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows n = 0..50)
Wikipedia, Jeson Mor.
FORMULA
T(n,k) = A049604(n, n-k) = A065775(n, n-k) for n > 1. - Andrew Howroyd, Feb 28 2020
EXAMPLE
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
CROSSREFS
KEYWORD
sign,look,tabl
AUTHOR
Felix Fröhlich, Dec 15 2016
EXTENSIONS
a(5) corrected and terms a(15) and beyond from Andrew Howroyd, Feb 28 2020
STATUS
approved