STATUS
proposed
approved
The OEIS is supported by the many generous donors to the OEIS Foundation.
Revision History for A255297
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Number of ON cells after n generations of the odd-rule cellular automaton defined by OddRule 035 when started with a single ON cell.
(history; published version)
(history; published version)
STATUS
editing
proposed
LINKS
Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, <a href="http://arxiv.org/abs/1503.01796">A Meta-Algorithm for Creating Fast Algorithms for Counting ON Cells in Odd-Rule Cellular Automata</a>, arXiv:1503.01796, [math.CO], 2015; see also the <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/CAcount.html">Accompanying Maple Package</a>.
N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168, [math.CO], 2015.
STATUS
proposed
editing
STATUS
editing
proposed
MATHEMATICA
a27649[n_] := 2(3^n) - 2^n;
Table[Times @@ (a27649[Length[#]]&) /@ Select[Split[IntegerDigits[n, 2]], #[[1]] == 1&], {n, 0, 59}] (* Jean-François Alcover, Sep 15 2018 *)
STATUS
approved
editing
STATUS
editing
approved
REFERENCES
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, Preprint, 2015.
LINKS
Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, <a href="http://arxiv.org/A160239abs/a160239_11503.txt01796Catalog of 3X3 A Meta-Algorithm for Creating Fast Algorithms for Counting ON Cells in Odd -Rule Cellular Automata</a>, arXiv:1503.01796, 2015; see also the <a href="http://www.math.rutgers.edu/~zeilberg/mamarim
Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, <a href="http://NeilSloanearxiv.comorg/docabs/Fredkin1503.pdf04249On the Number of ON Cells in Odd-Rule Cellular Automata on the Square Grid</a>, arXiv:1503.04249, 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: <a href="https://vimeo.com/119073818">Part 1</a>, <a href="https://vimeo.com/119073819">Part 2</a>
N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168, 2015
STATUS
approved
editing
STATUS
editing
approved
NAME
4d
Number of ON cells after n generations of the odd-rule cellular automaton defined by OddRule 035 when started with a single ON cell.
REFERENCES
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, Preprint, 2015.
LINKS
N. J. A. Sloane, <a href="/A160239/a160239_1.txt">Catalog of 3X3 Odd Rule Cellular Automata</a>
N. J. A. Sloane, <a href="http://NeilSloane.com/doc/Fredkin.pdf">On the Number of ON Cells in Cellular Automata</a>, 2015
<a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
FORMULA
Run length transform of A027649.
CROSSREFS
Cf. A027649.
AUTHOR
N. J. A. Sloane, and _Doron Zeilberger_, Feb 23 2015
STATUS
approved
editing
STATUS
editing
approved