2$), type {\tt ezraG();} \quad . To get instructions on using a particular procedure, type {\tt ezra(ProcedureName);} \quad . For example. procedure {\tt CAaut} finds the recurrence `automaton', and to get help with it, type {\tt ezra(CAaut);} \quad . For our toy example, type {\tt CAaut([1+x+x**2,1],[x],2,2);} which produces as output the pair {\tt [[[[1], [2, 1]], [[1, 1], [1, 1]]], [1, 2]]} \quad, where the first component, {\tt [[[1], [2, 1]], [[1, 1], [1, 1]]]} \quad , is Maple's way of encoding the recurrence $$ a_1(2n)=a_1(n) \quad , \quad a_1(2n+1)=a_2(n)+a_1(n) \quad ; \quad a_2(2n)=a_1(n)+a_1(n) \quad , \quad a_2(2n+1)=a_1(n)+a_1(n) \quad . $$ The second component {\tt [1, 2]} is Maple's way of encoding the initial conditions $$ a_1(1)= 1 \quad, \quad a_2(1)=2 \quad . $$ Procedure {\tt SeqF} uses the scheme, once found, to compute as many terms as desired, while procedure {\tt ARLT} (for {\it anti-run-length-transform}, see [Sl]) computes the sparse subsequence in the places $p^i-1$. Procedure {\tt GFsP} finds the {\bf proved} generating function for that subsequence, and if the size of the system is too big, {\tt GFsG} guesses it faster, and as we mentioned above, the guess can be justified {\it a posteriori}. {\bf References} [3by3] Shalosh B. Ekhad, N.~J.~A.~Sloane, and Doron Zeilberger, {\it ``Odd-Rule'' Cellular Automata on the Square Grid}, in preparation, March 2015. [OEIS] The OEIS Foundation Inc., {\it The On-Line Encyclopedia of Integer Sequences}, {\tt https://oeis.org}. [RZ] Eric Rowland and Doron Zeilberger, {\it A Case Study in Meta-AUTOMATION: AUTOMATIC Generation of Congruence AUTOMATA For Combinatorial Sequences}, J. Difference Equations and Applications {\bf 20} (2014), 973--988; \hfill\break {\tt http://www.math.rutgers.edu/\~{}zeilberg/mamarim/mamarimhtml/meta.html}. [SaZ] Bruno Salvy and Paul Zimmermann, {\it GFUN: a Maple package for the Manipulation of Generating and Holonomic Functions in One Variable}, ACM Trans. Math. Software {\bf 20} (1994), 163--177. [Sl] N. J. A. Sloane {\it On the Number of ON Cells in Cellular Automata}, 2015; \hfill\break {\tt http://arxiv.org/abs/1503.01168}. \bigskip \bigskip \hrule \bigskip Shalosh B. Ekhad, c/o D. Zeilberger, Department of Mathematics, Rutgers University (New Brunswick), Hill Center-Busch Campus, 110 Frelinghuysen Rd., Piscataway, NJ 08854-8019, USA. \bigskip \hrule \bigskip N. J. A. Sloane, The OEIS Foundation Inc, 11 South Adelaide Ave, Highland Park, NJ 08904, USA, and Department of Mathematics, Rutgers University (New Brunswick); \hfill \break njasloane at gmail dot com \quad ; \quad {\tt http://neilsloane.com/ } \quad . \bigskip \hrule \bigskip Doron Zeilberger, Department of Mathematics, Rutgers University (New Brunswick), Hill Center-Busch Campus, 110 Frelinghuysen Rd., Piscataway, NJ 08854-8019, USA; \hfill \break zeilberg at math dot rutgers dot edu \quad ; \quad {\tt http://www.math.rutgers.edu/\~{}zeilberg/} \quad . \bigskip \hrule \bigskip \bigskip Published in The Personal Journal of Shalosh B. Ekhad and Doron Zeilberger \hfill \break ({\tt http://www.math.rutgers.edu/\~{}zeilberg/pj.html}), N.~J.~A.~Sloane's home page \hfill \break ({\tt http://neilsloane.com/}), and {\tt arxiv.org} \quad . \bigskip \bigskip \hrule \bigskip {\bf Mar 05, 2015} \end