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A255462 Number of ON cells after n generations of the odd-rule 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 (list; graph; refs; listen; history; text; internal format)
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 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

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

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Last modified December 10 20:46 EST 2017. Contains 295855 sequences.