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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

%I #17 Oct 28 2021 07:10:25

%S 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

%N 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.

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

%e Table begins:

%e 1;

%e 2, 4;

%e 3, 5, 9;

%e 4, 8, 11, 16;

%e 5, 9, 14, 19, 25;

%e 6, 12, 18, 24, 29, 36;

%Y Cf. A324604.

%K tabl,nonn,more,walk

%O 1,2

%A _Peter Kagey_, Mar 09 2019