A306779 Table read by rows: T(n,k) is the length of the longest non-intersecting loop starting at (0,0) on the n X k torus consisting of steps up and to the right, 1 <= k <= n.

1, 2, 4, 3, 5, 9, 4, 8, 11, 16, 5, 9, 14, 19, 25, 6, 12, 18, 24, 29, 36, 7, 13, 19, 27, 33, 41

Offset

1,2

Comments

Conjecture: T(n,k) = n*k if and only if k = 1 or gcd(n,k) > 1.

Links

Table of n, a(n) for n=1..27.

Example

Table begins:
  1;
  2,  4;
  3,  5,  9;
  4,  8, 11, 16;
  5,  9, 14, 19, 25;
  6, 12, 18, 24, 29, 36;

Crossrefs

Cf. A324604.

Sequence in context: A243573 A132193 A185910 * A349947 A351652 A333087

Adjacent sequences: A306776 A306777 A306778 * A306780 A306781 A306782

Keyword

tabl,nonn,more,walk

Author

Peter Kagey, Mar 09 2019

Status

approved