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

1,3

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

Example

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, ...

Crossrefs

Half of A064298.

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

Right hand column is A007764.

Cf. A271465.

Sequence in context: A205870 A371062 A354116 * A358501 A323493 A052661

Adjacent sequences: A064294 A064295 A064296 * A064298 A064299 A064300

Keyword

nonn,tabl

Author

Henry Bottomley, Sep 05 2001

Status

approved