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.

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, 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, 7, 6, 7, 6, 7, 6, 7, 8, 7, 8, 6, 7, 6, 7, 6, 7, 6, 7, 8, 7, 8, 9, 8

Offset

0,2

Comments

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

References

Fred Lunnon, Knights in Daze, to appear.

Links

Alois P. Heinz, Rows n = 0..140, flattened

Fred Lunnon, Revised tables & functions for knight's path distance and count (MAGMA code)

Formula

See A065775.

Example

Triangle starts:
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,
5,4,5,4,5,4,5,6,
4,5,4,5,4,5,6,5,6,
5,6,5,6,5,6,5,6,7,6
...
See examples under A242511.

Prog

(Magma) // See link for recursive & explicit algorithms. - Fred Lunnon, May 18 2014

Crossrefs

Cf. A065775, A183044, A183045, A183046, A018837, A018839, A242511, A242512, A242513, A242514, A242591.

Sequence in context: A164585 A200996 A154364 * A050604 A262672 A252731

Adjacent sequences: A183040 A183041 A183042 * A183044 A183045 A183046

Keyword

nonn,tabl

Author

Clark Kimberling, Dec 20 2010

Extensions

Edited by N. J. A. Sloane, May 23 2014

Offset corrected by Alois P. Heinz, Sep 10 2014

Status

approved