A324604 Table read by rows: T(n,k) is the number of non-intersecting loops starting at (0,0) on the n X k torus consisting of steps up and to the right, 1 <= k <= n.

2, 2, 4, 2, 7, 22, 2, 13, 66, 258, 2, 25, 189, 898, 3528, 2, 49, 537, 3118, 14545, 87830, 2, 97, 1544, 11462, 75446, 746589, 8295536, 2, 193, 4508, 44990, 447667

Offset: 1

Author

Peter Kagey, Mar 09 2019

Keywords

• tabl
• more
• nonn
• walk

Comments

Conjecture: Second column is A181565.

Examples

			The T(3,2) = 7 walks on the 3 X 2 torus are:
  (0,0),(0,1),(0,0)
  (0,0),(1,0),(2,0),(0,0)
  (0,0),(0,1),(1,1),(1,0),(2,0),(0,0)
  (0,0),(0,1),(1,1),(2,1),(2,0),(0,0)
  (0,0),(1,0),(1,1),(2,1),(0,1),(0,0)
  (0,0),(1,0),(1,1),(2,1),(2,0),(0,0)
  (0,0),(1,0),(2,0),(2,1),(0,1),(0,0)
Table begins:
  2
  2,  4,
  2,  7,   22,
  2, 13,   66,   258,
  2, 25,  189,   898,  3528,
  2, 49,  537,  3118, 14545,  87830,
  2, 97, 1544, 11462, 75446, 746589, 8295536
		

Links

• Peter Kagey, Cycles on the torus, Programming Puzzles & Code Golf Stack Exchange.

Crossrefs

Cf. A181565, A324603.