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.

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

Offset

2,1

Comments

The triangle T(n,k) is:

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

-+--------------------------

2| 3

3| 5 7

4| 6 9 11

5| 8 11 14 17

6| 9 14 17 21 24

7| 11 16 20 24 29 33

8| 12 18 22 27 32 38 42

9| 14 20 25 30 36 42 48 53

Reading this triangle by rows gives the sequence.

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

Links

Table of n, a(n) for n=2..37.

C. H. Gribble, Computed characteristics of complete non-self-adjacent paths in a square lattice bounded by various sizes of rectangle.

C. H. Gribble, Computes characteristics of complete non-self-adjacent paths in square and cubic lattices bounded by various sizes of rectangle and rectangular cuboid respectively.

Example

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

Crossrefs

Cf. A213106, A213249.

Sequence in context: A071581 A184722 A219781 * A084393 A100005 A215457

Adjacent sequences: A215104 A215105 A215106 * A215108 A215109 A215110

Keyword

nonn,tabl,more

Author

Christopher Hunt Gribble, Aug 03 2012

Status

approved