OFFSET
1,1
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).
CROSSREFS
KEYWORD
nonn
AUTHOR
Tom Womack (tom(AT)womack.net)
EXTENSIONS
More terms from Hagen von Eitzen, Oct 21 2009
STATUS
approved