A243302 Consider a triangular Go board graph with side length n; remove i nodes and let j be the number of nodes in the largest connected subgraph remaining; then a(n) = minimum (i + j).

1, 3, 4, 6, 9, 11, 14, 18, 21, 25

Offset

1,2

Comments

Maximum number of boat shapes formed from six equilateral triangles that can be placed in an equilateral triangle of order a(n+4). - Craig Knecht, Sep 13 2017

Links

Table of n, a(n) for n=1..10.

Gordon Hamilton, Children working on this problem in grade 2 classrooms

Craig Knecht, Maximum number of six triangle boat shapes in a equilateral triangle.

Example

a(11) <= 29 because i = 20 and j = 9 in the following graph:
            -
           - -
          - - -
         X - - X
        - X - X -
       - - X X - -
      - - X - X - -
     X X X - - X X X
    - - - X - X - - -
   - - - X - - X - - -
  - - - X - - - X - - -
a(11) <= 29 because i = 16 and j = 13 in the following graph:
            -
           - -
          - - -
         - - - -
        X X - - -
       - - X X X X
      - - X - X - -
     - - X - - X - -
    - - X - - - X - -
   - - X - - - X - - -
  - - X - - - X - - - -

Crossrefs

For square graphs see A243205.

Cf. A301654.

Sequence in context: A285412 A105527 A094345 * A301654 A289233 A039889

Adjacent sequences: A243299 A243300 A243301 * A243303 A243304 A243305

Keyword

nonn,more

Author

Gordon Hamilton, Jun 03 2014

Status

approved