

A255462


Number of ON cells after n generations of the oddrule cellular automaton defined by OddRule 365 when started with a single ON cell.


2



1, 6, 6, 30, 6, 36, 30, 138, 6, 36, 36, 180, 30, 180, 138, 606, 6, 36, 36, 180, 36, 216, 180, 828, 30, 180, 180, 900, 138, 828, 606, 2586, 6, 36, 36, 180, 36, 216, 180, 828, 36, 216, 216, 1080, 180, 1080, 828, 3636, 30, 180, 180, 900, 180, 1080, 900, 4140, 138, 828, 828, 4140
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OFFSET

0,2


LINKS

Paul Tek, Table of n, a(n) for n = 0..10000
Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, A MetaAlgorithm for Creating Fast Algorithms for Counting ON Cells in OddRule Cellular Automata, arXiv:1503.01796 [math.CO], 2015; see also the Accompanying Maple Package.
Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, OddRule 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
N. J. A. Sloane, Illustration of generations 0 to 15
N. J. A. Sloane, Illustration of generations 0 to 35
N. J. A. Sloane, Illustration of generation 7
N. J. A. Sloane, Illustration of generation 15
N. J. A. Sloane, Mathematica notebook to generate this cellular automaton
Index entries for sequences related to cellular automata


FORMULA

It follows from Theorem 3 of the Fredkin.pdf (2015) paper that this satisfies the recurrence a(2t)=a(t), a(4t+1)=6*a(t), and a(4t+3)=7*a(2t+1)12*a(t) for t>0, with a(0)=1.  N. J. A. Sloane, Mar 10 2015


EXAMPLE

From Omar E. Pol, Sep 08 2016: (Start)
Written as an irregular triangle in which the row lengths are the terms of A011782 the sequence begins:
1;
6;
6, 30;
6, 36, 30, 138;
6, 36, 36, 180, 30, 180, 138, 606;
6, 36, 36, 180, 36, 216, 180, 828, 30, 180, 180, 900, 138, 828, 606, 2586;
...
Right border gives A255463. (End)


MATHEMATICA

(* See Mathematica notebook in link *)
(* or *)
A255462[n_] := Total[CellularAutomaton[{42, {2, {{0, 1, 1}, {1, 1, 0}, {1, 0, 1}}}, {1, 1}}, {{{1}}, 0}, {{{n}}}], 2]; Array[A255462, 60, 0] (* JungHwan Min, Sep 06 2016 *)
A255462L[n_] := Total[#, 2] & /@ CellularAutomaton[{42, {2, {{0, 1, 1}, {1, 1, 0}, {1, 0, 1}}}, {1, 1}}, {{{1}}, 0}, n]; A255462L[59] (* JungHwan Min, Sep 06 2016 *)


CROSSREFS

Run length transform of A255463.
Sequence in context: A016725 A267651 A151779 * A066714 A054436 A055522
Adjacent sequences: A255459 A255460 A255461 * A255463 A255464 A255465


KEYWORD

nonn,tabf,look


AUTHOR

N. J. A. Sloane and Doron Zeilberger, Feb 23 2015


STATUS

approved



