A351388 Maximum k for which the grid graph P_2 X P_k is a subgraph of the n X n knight graph.

1, 2, 7, 10, 15, 22, 29, 36, 46

Offset

3,2

Comments

a(12) >= 57.

Links

Table of n, a(n) for n=3..11.

Donald E Knuth, The Art of Computer Programming, exercises on "knight grids" in Section 7.2.2.3 (preliminary draft)

Don Knuth, CWEB program

Example

a(5) = 7 because of the following embedding of P2 X P7 into N5:
  - - 6 1 -
  6 1 3 - 5  where the vertices of P2 X P7 are
  3 - 5 7 2     1 2 3 4 5 6 7
  - 7 2 4 -     1 2 3 4 5 6 7
  - 4 - - -

Crossrefs

Cf. A351391 (considers induced subgraphs), A351389 (considers P3 X Pk), A351390 (considers P4 X Pk).

Sequence in context: A190375 A066097 A035336 * A246128 A343990 A226830

Adjacent sequences: A351385 A351386 A351387 * A351389 A351390 A351391

Keyword

nonn,more

Author

Don Knuth, Feb 10 2022

Status

approved