cp's OEIS Frontend

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.

%I A279605 #22 Apr 13 2020 01:39:30
%S A279605 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,
%T A279605 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,
%U A279605 7,8,7,6,7,6,7,6,7,6,7,8,9,8,7,8,7,6,7,6,7,6,7,6
%N 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.
%H A279605 Andrew Howroyd, <a href="/A279605/b279605.txt">Table of n, a(n) for n = 0..1325</a> (rows n = 0..50)
%H A279605 Wikipedia, <a href="http://en.wikipedia.org/wiki/Jeson_Mor">Jeson Mor</a>.
%F A279605 T(n,k) = A049604(n, n-k) = A065775(n, n-k) for n > 1. - _Andrew Howroyd_, Feb 28 2020
%e A279605 Triangle starts
%e A279605    0;
%e A279605   -1, -1;
%e A279605    4,  1,  2;
%e A279605    2,  3,  2,  3;
%e A279605    4,  3,  2,  3,  2;
%e A279605    4,  3,  4,  3,  4,  3;
%e A279605    4,  5,  4,  3,  4,  3,  4;
%e A279605    6,  5,  4,  5,  4,  5,  4,  5;
%e A279605    6,  5,  6,  5,  4,  5,  4,  5,  4;
%e A279605    6,  7,  6,  5,  6,  5,  6,  5,  6,  5;
%e A279605    ...
%e A279605 T(0, 1) = 0, because the board has just 1 square where the knight must start.
%e A279605 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.
%e A279605 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.
%e A279605 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
%Y A279605 Cf. A035008, A049604, A065775.
%K A279605 sign,look,tabl
%O A279605 0,4
%A A279605 _Felix Fröhlich_, Dec 15 2016
%E A279605 a(5) corrected and terms a(15) and beyond from _Andrew Howroyd_, Feb 28 2020