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A183043 Triangular array, T(i,j)=number of knight's moves to points on vertical segments (n,0), (n,1),...,(n,n) on infinite chessboard.

%I A183043 #21 Mar 31 2024 12:04:42
%S A183043 0,3,2,2,1,4,3,2,3,2,2,3,2,3,4,3,4,3,4,3,4,4,3,4,3,4,5,4,5,4,5,4,5,4,
%T A183043 5,6,4,5,4,5,4,5,6,5,6,5,6,5,6,5,6,5,6,7,6,6,5,6,5,6,5,6,7,6,7,8,7,6,
%U A183043 7,6,7,6,7,6,7,8,7,8,6,7,6,7,6,7,6,7,8,7,8,9,8
%N A183043 Triangular array, T(i,j)=number of knight's moves to points on vertical segments (n,0), (n,1),...,(n,n) on infinite chessboard.
%C A183043 Stated another way, T(n,k) = distance from square (0,0) at center of an infinite open chessboard to square (n,k) via shortest knight path, for 0<=k<=n. - _Fred Lunnon_, May 18 2014
%D A183043 Fred Lunnon, Knights in Daze, to appear.
%H A183043 Alois P. Heinz, <a href="/A183043/b183043.txt">Rows n = 0..140, flattened</a>
%H A183043 Fred Lunnon, <a href="/A242591/a242591.a.txt">Revised tables & functions for knight's path distance and count (MAGMA code)</a>
%F A183043 See A065775.
%e A183043 Triangle starts:
%e A183043 0,
%e A183043 3,2,
%e A183043 2,1,4,
%e A183043 3,2,3,2,
%e A183043 2,3,2,3,4,
%e A183043 3,4,3,4,3,4,
%e A183043 4,3,4,3,4,5,4,
%e A183043 5,4,5,4,5,4,5,6,
%e A183043 4,5,4,5,4,5,6,5,6,
%e A183043 5,6,5,6,5,6,5,6,7,6
%e A183043 ...
%e A183043 See examples under A242511.
%o A183043 (Magma) // See link for recursive & explicit algorithms. - _Fred Lunnon_, May 18 2014
%Y A183043 Cf. A065775, A183044, A183045, A183046, A018837, A018839, A242511, A242512, A242513, A242514, A242591.
%K A183043 nonn,tabl
%O A183043 0,2
%A A183043 _Clark Kimberling_, Dec 20 2010
%E A183043 Edited by _N. J. A. Sloane_, May 23 2014
%E A183043 Offset corrected by _Alois P. Heinz_, Sep 10 2014