A060521 Number of 3 X n grids of black and white cells, no 3 of same color vertically or horizontally contiguous.

6, 36, 102, 378, 1260, 4374, 14946, 51384, 176238, 605022, 2076288, 7126302, 24457806, 83942100, 288096942, 988778082, 3393583068, 11647114446, 39974047290, 137194888728, 470866430838, 1616060190870, 5546478488640

Offset: 1

Author

Tom Womack (tom(AT)womack.net)

Keywords

• nonn

Comments

The conjectured recursion is correct: For each n count the solutions separately where the last two rows differ in 0, 1, 2, or 3 places; a linear recursion is then readily found. The corresponding matrix has characteristic polynomial x^4 - 2 x^3 - 5 x^2 + 1, matching the recursion recursion a(n+4) = 2a(n+3) + 5a(n+2) - a(n). [From Hagen von Eitzen, Oct 21 2009]

Links

• Robert Dougherty-Bliss, Christoph Koutschan, Natalya Ter-Saakov, and Doron Zeilberger, The (Symbolic and Numeric) Computational Challenges of Counting 0-1 Balanced Matrices, arXiv:2410.07435 [math.CO], 2024. See p. 6.

Formula

Almost surely satisfies a(n+4) = 2a(n+3) + 5a(n+2) - a(n).

Extensions

More terms from Hagen von Eitzen, Oct 21 2009