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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
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified October 25 13:27 EDT 2021. Contains 348252 sequences. (Running on oeis4.)