

A215107


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


0



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
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OFFSET

2,1


COMMENTS

The triangle T(n,k) is:
....k..2..3..4..5..6..7..8..9
.n
.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) <= ceil(3nk/4).


LINKS

Table of n, a(n) for n=2..37.
C. H. Gribble, Computed characteristics of complete nonselfadjacent paths in a square lattice bounded by various sizes of rectangle.
C. H. Gribble, Computes characteristics of complete nonselfadjacent 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 nonselfadjacent 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


AUTHOR

Christopher Hunt Gribble, Aug 03 2012


STATUS

approved



