A064297 Triangle of self-avoiding rook paths joining opposite corners of n X k board.

1, 1, 2, 1, 4, 12, 1, 8, 38, 184, 1, 16, 125, 976, 8512, 1, 32, 414, 5382, 79384, 1262816, 1, 64, 1369, 29739, 752061, 20562673, 575780564, 1, 128, 4522, 163496, 7110272, 336067810, 16230458696, 789360053252, 1, 256, 14934, 896476, 67005561

Offset: 1

Author

Henry Bottomley, Sep 05 2001

Keywords

• nonn
• tabl

Examples

			Triangle starts
1,
1, 2,
1, 4, 12,
1, 8, 38, 184,
1, 16, 125, 976, 8512,
1, 32, 414, 5382, 79384, 1262816,
1, 64, 1369, 29739, 752061, 20562673, 575780564,
1, 128, 4522, 163496, 7110272, 336067810, ...
		

References

• S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 331-339.

Links

• Ruben Grønning Spaans, Triangle of rows 1 to 20, flattened
• Steven R. Finch, Self-Avoiding Walks of a Rook on a Chessboard [From Steven Finch, Apr 20 2019]
• Steven R. Finch, Self-Avoiding Walks of a Rook [From Steven Finch, Apr 20 2019; mentioned in Finch's "Gammel" link above]
• Steven R. Finch, Table of Non-Overlapping Rook Paths [From Steven Finch, Apr 20 2019; mentioned in Finch's "Gammel" link above]
• Ruben Grønning Spaans, C program

Crossrefs

Half of A064298.

Row/column combinations include A000012, A000079, A006192, A007786, A007787, A145403.

Right hand column is A007764.

Cf. A271465.