A183045 -id:A183045 - cp's OEIS frontend

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

Clark Kimberling, Dec 20 2010

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

			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.

Fred Lunnon, Knights in Daze, to appear.

Alois P. Heinz, Rows n = 0..140, flattened
Fred Lunnon, Revised tables & functions for knight's path distance and count (MAGMA code)

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

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

See A065775.

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

Offset corrected by Alois P. Heinz, Sep 10 2014

A183046 Sums of knight's moves from (0,0) to vertical segments (n,-n) to (n,n) on infinite chessboard.

Original entry on oeis.org

0, 7, 12, 17, 26, 39, 50, 71, 84, 109, 128, 157, 178, 215, 238, 279, 308, 353, 384, 437, 470, 527, 566, 627, 668, 737, 780, 853, 902, 979, 1030, 1115, 1168, 1257, 1316, 1409, 1470, 1571, 1634, 1739, 1808, 1917, 1988, 2105

Offset: 0

Clark Kimberling, Dec 20 2010

nonn

Cf.A065775, A183045.

T(n,-n)+T(n,-n+1)+...+T(n,n), where T is given at A065775.

Empirical g.f.: x*(4*x^8+2*x^7-8*x^6-7*x^5+5*x^3-3*x^2-12*x-7) / ((x-1)^3*(x+1)^2*(x^2+x+1)). - Colin Barker, May 04 2014

cp's OEIS Frontend

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.

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