A306779 -id:A306779 - cp's OEIS frontend

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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.

Original entry on oeis.org

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

Peter Kagey, Mar 09 2019

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.

			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;

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

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

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