A269516 Number of T(n) X T(n) matrices containing the multiset {1, 2, 2, 3, 3, 3, ..., n, n, ..., n} in each row and column, where T(n) = A000217(n).

1, 6, 5450400

Offset

1,2

Comments

Each 1 <= k <= n appears k times in the multiset. Terms include rotations/reflections. Related to Latin squares. Inspired by related question in "Chess Set Latin Square" link.

Links

Table of n, a(n) for n=1..3.

Mathematics Stack Exchange, Chess Set Latin Square

Example

The a(3) = 5450400 (= 6!*7570) 6 X 6 matrices include
  1 2 2 3 3 3
  2 1 2 3 3 3
  2 2 1 3 3 3
  3 3 3 1 2 2
  3 3 3 2 1 2
  3 3 3 2 2 1.
Using terminology such as that suggested by Rebecca J. Stones in a "Chess Set Latin Square" comment, this matrix is a (3, 2, 1)-frequency square corresponding to a decomposition of K_{6,6} into one 3-regular spanning subgraph, one 2-regular spanning subgraph, and one 1-regular spanning subgraph.

Crossrefs

Cf. A022915 (includes linear arrangements of same multisets), A000217, A002860.

Sequence in context: A115476 A297528 A172876 * A116272 A273723 A182792

Adjacent sequences: A269513 A269514 A269515 * A269517 A269518 A269519

Keyword

nonn,bref,hard,more

Author

Rick L. Shepherd, Feb 28 2016

Status

approved