A060521 - OEIS

A060521

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

%I #9 Oct 14 2024 12:17:32

%S 6,36,102,378,1260,4374,14946,51384,176238,605022,2076288,7126302,

%T 24457806,83942100,288096942,988778082,3393583068,11647114446,

%U 39974047290,137194888728,470866430838,1616060190870,5546478488640

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

%C 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]

%H Robert Dougherty-Bliss, Christoph Koutschan, Natalya Ter-Saakov, and Doron Zeilberger, <a href="https://arxiv.org/abs/2410.07435">The (Symbolic and Numeric) Computational Challenges of Counting 0-1 Balanced Matrices</a>, arXiv:2410.07435 [math.CO], 2024. See p. 6.

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

%K nonn

%O 1,1

%A Tom Womack (tom(AT)womack.net)

%E More terms from _Hagen von Eitzen_, Oct 21 2009