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.

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

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: A267651 A016725 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