This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A246034 Number of odd terms in f^n, where f = x^4*y^4 + x^4*y^3 + x^3*y^4 + x^4*y^2 + x^2*y^4 + x^4*y + x^3*y^2 + x^2*y^3 + x*y^4 + x^4 + x^2*y^2 + y^4 + x^3 + x^2*y + x*y^2 + y^3 + x^2 + y^2 + x + y + 1. 9
 1, 21, 21, 85, 21, 233, 85, 321, 21, 441, 233, 761, 85, 1137, 321, 1545, 21, 441, 441, 1785, 233, 2925, 761, 3589, 85, 1785, 1137, 3977, 321, 4549, 1545, 5909, 21, 441, 441, 1785, 441, 4893, 1785, 6741, 233, 4893, 2925, 9949, 761, 11301, 3589, 13181, 85, 1785, 1785 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This is the number of ON cells in a certain 2-D CA in which the neighborhood of a cell is defined by f, and in which a cell is ON iff there was an odd number of ON cells in the neighborhood at the previous generation. LINKS Shalosh B. Ekhad, N. J. A. Sloane, and  Doron Zeilberger, A Meta-Algorithm for Creating Fast Algorithms for Counting ON Cells in Odd-Rule Cellular Automata, arXiv:1503.01796 [math.CO], 2015; see also the Accompanying Maple Package. Shalosh B. Ekhad, N. J. A. Sloane, and  Doron Zeilberger, Odd-Rule Cellular Automata on the Square Grid, arXiv:1503.04249 [math.CO], 2015. N. J. A. Sloane, On the No. of ON Cells in Cellular Automata, Video of talk in Doron Zeilberger's Experimental Math Seminar at Rutgers University, Feb. 05 2015: Part 1, Part 2 N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015. EXAMPLE Here is the neighborhood: [X, X, X, X, X] [X, 0, X, 0, X] [X, X, X, X, X] [X, 0, X, 0, X] [X, X, X, X, X] which contains a(1) = 21 ON cells. MAPLE C:=f->subs({x=1, y=1}, f); # Find number of ON cells in CA for generations 0 thru M defined by rule # that cell is ON iff number of ON cells in nbd at time n-1 was odd # where nbd is defined by a polynomial or Laurent series f(x, y). OddCA:=proc(f, M) global C; local n, a, i, f2, p; f2:=simplify(expand(f)) mod 2; a:=[]; p:=1; for n from 0 to M do a:=[op(a), C(p)]; p:=expand(p*f2) mod 2; od: lprint([seq(a[i], i=1..nops(a))]); end; f:=x^4*y^4+x^4*y^3+x^3*y^4+x^4*y^2+x^2*y^4+x^4*y+x^3*y^2+x^2*y^3+x*y^4+x^4+    x^2*y^2+y^4+x^3+x^2*y+x*y^2+y^3+x^2+y^2+x+y+1; OddCA(f, 100); MATHEMATICA f = x^4*y^4 + x^4*y^3 + x^3*y^4 + x^4*y^2 + x^2*y^4 + x^4*y + x^3*y^2 + x^2*y^3 + x*y^4 + x^4 + x^2*y^2 + y^4 + x^3 + x^2*y + x*y^2 + y^3 + x^2 + y^2 + x + y + 1; a[0] = 1; a[n_] := Count[List @@ Expand[f^n] /. {x -> 1, y -> 1}, _?OddQ]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Dec 11 2017 *) CROSSREFS Other CA's that use the same rule but with different cell neighborhoods: A160239, A102376, A071053, A072272, A001316, A246035. Sequence in context: A040421 A022355 A048245 * A220689 A056485 A056475 Adjacent sequences:  A246031 A246032 A246033 * A246035 A246036 A246037 KEYWORD nonn AUTHOR N. J. A. Sloane, Aug 20 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 6 04:43 EST 2019. Contains 329784 sequences. (Running on oeis4.)