A242591 Triangle of number of shortest knight paths T(n,k) from square (0,0) at center of an infinite open chessboard to square (n,k), for 0 <= k <= n.

1, 12, 2, 2, 1, 54, 6, 2, 9, 2, 2, 6, 1, 3, 32, 6, 28, 6, 24, 3, 8, 24, 3, 18, 1, 12, 85, 6, 100, 16, 95, 12, 60, 4, 25, 240, 6, 70, 4, 50, 1, 30, 201, 10, 60, 40, 330, 35, 266, 20, 150, 5, 66, 588, 20, 210, 10, 180, 5, 120, 1, 60, 462, 15, 147, 1512

Offset: 0

Author

Fred Lunnon, May 18 2014

Keywords

• easy
• nonn
• walk
• tabl

Examples

			Triangle starts:
    1;
   12,   2;
    2,   1, 54;
    6,   2,  9,   2;
    2,   6,  1,   3, 32;
    6,  28,  6,  24,  3,   8;
   24,   3, 18,   1, 12,  85,   6;
  100,  16, 95,  12, 60,   4,  25, 240;
    6,  70,  4,  50,  1,  30, 201,  10,  60;
   40, 330, 35, 266, 20, 150,   5,  66, 588, 20;
  ...
See examples under A242511.
		

Links

• Georg Fischer, Table of n, a(n) for n = 0..209
• Fred Lunnon, Revised tables & functions for knight's path distance and count (MAGMA code)

Crossrefs

Cf. A242511, A242512, A242513, A242514, A183043.

Programs

Magma

// See attached a-file for recursive & explicit algorithms.

Extensions

a(66) ff. exported to b-file by Georg Fischer, Jul 16 2020