A381553 Number of 2*n X 6 binary arrays with row sums 3 and column sums n, avoiding the patterns 010 and 101 in any row and column.

1, 8, 64, 368, 2776, 25880, 251704, 2629080, 28964248, 331032312, 3907675376, 47392320240, 587548108400, 7421689479608, 95248568409312, 1239031994818680, 16306127772957216, 216760982171930144, 2906731043068293952, 39278080769921432856, 534346120254755625336

Offset

0,2

Links

Christoph Koutschan, Table of n, a(n) for n = 0..70

Robert Dougherty-Bliss, Christoph Koutschan, Natalya Ter-Saakov, and Doron Zeilberger, The (Symbolic and Numeric) Computational Challenges of Counting 0-1 Balanced Matrices, Enumerative Combinatorics and Applications 5:2, Article #S2R14, 2025.

Example

A few solutions for n = 3 are:
  0 0 0 1 1 1   0 0 0 1 1 1   0 0 0 1 1 1   0 0 0 1 1 1   0 0 0 1 1 1
  0 0 0 1 1 1   0 0 0 1 1 1   0 0 0 1 1 1   0 0 0 1 1 1   0 0 0 1 1 1
  0 0 0 1 1 1   0 0 1 1 1 0   0 1 1 0 0 1   0 1 1 1 0 0   1 0 0 0 1 1
  1 1 1 0 0 0   1 1 1 0 0 0   1 1 1 0 0 0   1 1 1 0 0 0   1 1 1 0 0 0
  1 1 1 0 0 0   1 1 1 0 0 0   1 1 1 0 0 0   1 1 1 0 0 0   1 1 1 0 0 0
  1 1 1 0 0 0   1 1 0 0 0 1   1 0 0 1 1 0   1 0 0 0 1 1   0 1 1 1 0 0

Crossrefs

Cf. A381551, A381554.

Sequence in context: A181480 A223948 A224151 * A225014 A228460 A202909

Adjacent sequences: A381550 A381551 A381552 * A381554 A381555 A381556

Keyword

nonn

Author

Christoph Koutschan, Feb 27 2025

Status

approved