A381551 -id:A381551 - cp's OEIS frontend

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

Christoph Koutschan, Feb 27 2025

nonn

			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

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.

Cf. A381551, A381554.

A381554 Number of 2*n X 8 binary arrays with row sums 4 and column sums n, avoiding the patterns 010 and 101 in any row and column.

Original entry on oeis.org

1, 18, 324, 2776, 34586, 575270, 10061200, 194929482, 4115573632, 91947761368, 2167131637540, 53550929019486, 1376887129235964, 36670419524921146, 1007581514656491404, 28454294028011307236, 823234343053953729538

Offset: 0

Christoph Koutschan, Feb 27 2025

nonn

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

Cf. A381551, A381553.

cp's OEIS Frontend

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.

Views

Author

Keywords

Examples

Links