A342936 Array T(n, k), n, k > 0, read by antidiagonals; T(n, k) is the number of rotationally symmetric self-avoiding rook paths joining opposite corners of an n X k board.

1, 1, 1, 1, 0, 1, 1, 2, 2, 1, 1, 0, 4, 0, 1, 1, 4, 6, 6, 4, 1, 1, 0, 13, 0, 13, 0, 1, 1, 8, 20, 34, 34, 20, 8, 1, 1, 0, 43, 0, 120, 0, 43, 0, 1, 1, 16, 66, 187, 320, 320, 187, 66, 16, 1, 1, 0, 142, 0, 1137, 0, 1137, 0, 142, 0, 1, 1, 32, 218, 1026, 3026, 5321, 5321, 3026, 1026, 218, 32, 1

Offset: 0

Author

Rémy Sigrist, Apr 11 2021

Keywords

• nonn
• tabl
• walk

Examples

			Array T(n, k) begins:
  n\k|  1   2    3     4      5      6       7        8         9
  ---+-----------------------------------------------------------
    1|  1   1    1     1      1      1       1        1         1
    2|  1   0    2     0      4      0       8        0        16
    3|  1   2    4     6     13     20      43       66       142
    4|  1   0    6     0     34      0     187        0      1026
    5|  1   4   13    34    120    320    1137     3026     10725
    6|  1   0   20     0    320      0    5321        0     87298
    7|  1   8   43   187   1137   5321   32916   152606    939548
    8|  1   0   66     0   3026      0  152606        0   7592509
    9|  1  16  142  1026  10725  87298  939548  7592509  81253506
		

Links

• Rémy Sigrist, Illustration of T(5, 6) = 320
• Rémy Sigrist, C program for A342936
• Index entries for sequences related to walks

Crossrefs

Cf. A064298.

Programs

C

See Links section.

Formula

T(n, k) <= A064298(n, k).

T(n, k) = T(k, n).

T(n, k) = 0 iff n and k are both even.

T(n, 1) = 1.

T(2*k+1, 2) = 2^k for any k >= 0.