On number of nonzero cells in some two-dimensional reversible   second-order cellular automata
  Recursive equations for the number of cells with nonzero values at $n$-th step for some two-dimensional reversible second-order cellular automata are proved in this work. Initial configuration is a single cell with the value one and all others zero. 
Alexander Yu. Vlasov
math.CO cs.DM nlin.CG