A337434 a(n) is the number of essentially different n X n matrices with maximal sum of entries satisfying the conditions of A228882.

1, 1, 1, 10, 20, 64

Offset

1,4

Comments

a(7) > 2630.

Links

Table of n, a(n) for n=1..6.

IBM Research, Maximal sum 6x6 grid, Ponder This December 2012.

Hugo Pfoertner, List of solutions for n=5 and n=6.

Example

a(1) = 1: the 8 rotated and reflected matrices are equivalent
  1 1   1 1    1 2   1 3    2 3   3 2    2 1   3 1
  2 3   3 2    1 3   1 2    1 1   1 1    3 1   2 1
.
a(3) = 1: due to mirror symmetry, there are only 4 equivalent matrices
  2 4 1    1 4 2    1 2 1    2 1 2
  1 3 2    2 3 1    4 3 4    4 3 4
  2 4 1    1 4 2    2 1 2    1 2 1
.
a(4) = 10:
  2 1 2 3    2 1 2 3    2 1 2 3    2 1 2 3    2 1 2 3
  3 4 2 1    3 4 5 1    3 4 5 1    3 5 2 1    3 5 4 1
  1 5 3 4    1 2 3 4    1 2 3 4    1 4 3 4    1 2 3 4
  3 2 1 2    2 3 1 2    3 2 1 2    3 2 1 2    2 3 1 2
.
  2 1 2 3    2 1 2 3    2 1 2 3    3 1 2 3    3 1 2 3
  3 5 4 1    4 3 4 1    4 3 5 1    2 3 3 1    2 3 3 1
  1 2 3 4    1 2 5 3    1 2 4 3    1 4 5 2    1 5 4 2
  3 2 1 2    2 3 1 2    2 3 1 2    3 2 1 3    3 2 1 3

Crossrefs

Cf. A228882.

Sequence in context: A294473 A174183 A267554 * A328490 A131726 A276764

Adjacent sequences: A337431 A337432 A337433 * A337435 A337436 A337437

Keyword

nonn,hard,more

Author

Hugo Pfoertner, Sep 22 2020

Status

approved