A381551 Number of 2*n X 4 binary arrays with row sums 2 and column sums n, avoiding the patterns 010 and 101 in any row and column.

1, 4, 16, 64, 324, 1764, 10000, 58564, 350464, 2131600, 13133376, 81757764, 513294336, 3245580900, 20646241344, 132021769104, 848031024996, 5468890936356, 35392361925904, 229761144199876, 1495753923300484, 9762043084514704, 63858040015802256

Offset: 0

Author

Christoph Koutschan, Feb 27 2025

Keywords

• nonn

Examples

			Here are 5 out of 16 solutions for n = 2:
  0 0 1 1   0 0 1 1   0 0 1 1   0 0 1 1   0 1 1 0
  0 0 1 1   0 1 1 0   1 0 0 1   1 1 0 0   1 0 0 1
  1 1 0 0   1 1 0 0   1 1 0 0   1 1 0 0   1 0 0 1
  1 1 0 0   1 0 0 1   0 1 1 0   0 0 1 1   0 1 1 0
the remaining ones are obtained from these by reflecting, rotating, or exchanging 0 and 1.
		

Links

• Christoph Koutschan, Table of n, a(n) for n = 0..1000
• 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.
• Christoph Koutschan, Recurrence of order 10 with polynomial coefficients of degree 21.

Crossrefs

Cf. A381553, A381554.

Formula

a(n) ~ 4*phi^(4*n)/(Pi*sqrt(5)*n), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Feb 27 2025