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A215107 Triangle read by rows: T(n,k) is the nodal length of the longest non-extendable (complete) non-self-adjacent simple path within a square lattice bounded by rectangles with nodal dimensions n and k, n >= k >= 2.

%I A215107 #10 Nov 25 2019 01:00:52
%S A215107 3,5,7,6,9,11,8,11,14,17,9,14,17,21,24,11,16,20,24,29,33,12,18,22,27,
%T A215107 32,38,42,14,20,25,30,36,42,48,53
%N A215107 Triangle read by rows: T(n,k) is the nodal length of the longest non-extendable (complete) non-self-adjacent simple path within a square lattice bounded by rectangles with nodal dimensions n and k, n >= k >= 2.
%C A215107 The triangle T(n,k) is:
%C A215107   n|k = 2  3  4  5  6  7  8  9
%C A215107   -+--------------------------
%C A215107   2|    3
%C A215107   3|    5  7
%C A215107   4|    6  9 11
%C A215107   5|    8 11 14 17
%C A215107   6|    9 14 17 21 24
%C A215107   7|   11 16 20 24 29 33
%C A215107   8|   12 18 22 27 32 38 42
%C A215107   9|   14 20 25 30 36 42 48 53
%C A215107 Reading this triangle by rows gives the sequence.
%C A215107 It appears that T(n,k) <= ceiling(3nk/4).
%H A215107 C. H. Gribble, <a href="https://oeis.org/wiki/Complete_non-self-adjacent_paths:Results_for_Square_Lattice">Computed characteristics of complete non-self-adjacent paths in a square lattice bounded by various sizes of rectangle.</a>
%H A215107 C. H. Gribble, <a href="https://oeis.org/wiki/Complete non-self-adjacent paths:Program">Computes characteristics of complete non-self-adjacent paths in square and cubic lattices bounded by various sizes of rectangle and rectangular cuboid respectively.</a>
%e A215107 T(2,2) = nodal length of the longest complete non-self-adjacent simple path within a 2 X 2 node rectangle.
%Y A215107 Cf. A213106, A213249.
%K A215107 nonn,tabl,more
%O A215107 2,1
%A A215107 _Christopher Hunt Gribble_, Aug 03 2012