A324605 Triangle read by rows: T(n,k) is the number of maximal-length 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, 1, 2, 1, 5, 6, 1, 2, 11, 8, 1, 9, 14, 19, 30, 1, 2, 3, 2, 29, 12, 1, 13, 76, 27, 99, 41, 126, 1, 2, 23, 8, 171

Offset: 1

Author

Peter Kagey, Mar 09 2019

Keywords

• nonn
• tabl
• more
• walk

Comments

Conjecture: T(2n,2) = 2 for all n.

Conjecture: T(2n+1,2) = 4n+1 for all n.

Conjecture: T(n,n) = A056188(n) for n > 1.

Examples

			Table begins:
  2;
  1,  2;
  1,  5,  6;
  1,  2, 11,  8;
  1,  9, 14, 19, 30;
  1,  2,  3,  2, 29, 12;
  1, 13, 76, 27, 99, 41, 126;
		

Crossrefs

Cf, A306779.

Formula

T(1,n) = 1 for n > 1.

T(n,n) is even for all n.