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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. 0

%I #10 Nov 25 2019 01:00:52

%S 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 32,38,42,14,20,25,30,36,42,48,53

%N 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 The triangle T(n,k) is:

%C n|k = 2 3 4 5 6 7 8 9

%C -+--------------------------

%C 2| 3

%C 3| 5 7

%C 4| 6 9 11

%C 5| 8 11 14 17

%C 6| 9 14 17 21 24

%C 7| 11 16 20 24 29 33

%C 8| 12 18 22 27 32 38 42

%C 9| 14 20 25 30 36 42 48 53

%C Reading this triangle by rows gives the sequence.

%C It appears that T(n,k) <= ceiling(3nk/4).

%H 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 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 T(2,2) = nodal length of the longest complete non-self-adjacent simple path within a 2 X 2 node rectangle.

%Y Cf. A213106, A213249.

%K nonn,tabl,more

%O 2,1

%A _Christopher Hunt Gribble_, Aug 03 2012

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)