login
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, 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
0,8
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.
EXAMPLE
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
PROG
(C) See Links section.
CROSSREFS
Cf. A064298.
Sequence in context: A290942 A039801 A105821 * A004564 A300705 A144157
KEYWORD
nonn,tabl,walk
AUTHOR
Rémy Sigrist, Apr 11 2021
STATUS
approved