login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A071044 Number of ON cells at generation n of 1-D CA defined by Rule 22, starting with a single ON cell. 3
1, 3, 2, 6, 2, 6, 4, 12, 2, 6, 4, 12, 4, 12, 8, 24, 2, 6, 4, 12, 4, 12, 8, 24, 4, 12, 8, 24, 8, 24, 16, 48, 2, 6, 4, 12, 4, 12, 8, 24, 4, 12, 8, 24, 8, 24, 16, 48, 4, 12, 8, 24, 8, 24, 16, 48, 8, 24, 16, 48, 16, 48, 32, 96, 2, 6, 4, 12, 4, 12, 8, 24, 4, 12, 8, 24, 8, 24, 16, 48 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Number of 1's in n-th row of triangle in A071029.
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.
LINKS
Kari Eloranta, Partially permutive cellular automata, Nonlinearity 6.6 (1993): 1009. (Further information about Rule 22)
Peter Grassberger, Long-range effects in an elementary cellular automaton, Journal of Statistical Physics, 45.1-2 (1986): 27-39. (Further information about Rule 22)
N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015.
S. Wolfram, Statistical mechanics of cellular automata, Rev. Mod. Phys., 55 (1983), 601--644.
FORMULA
If the binary expansion of n is b_{r-1} b_{r-2} ... b_2 b_1 b_0, then a(n) = 3^b_0 * Prod_{i=1..r-1} 2^b_i = 2^wt(n) if n is even, or (3/2)*2^wt(n) if n is odd (cf. A000120). - N. J. A. Sloane, Aug 09 2014
G.f. = (1+3*x)*Prod_{k >= 1} (1+2*x^(2^k)). - N. J. A. Sloane, Aug 09 2014
EXAMPLE
From Michael De Vlieger, Oct 05 2015: (Start)
First 8 rows, replacing "0" with "." for better visibility of ON cells, total of ON cells in each row to the left of the diagram:
1 1
3 1 1 1
2 1 . . . 1
6 1 1 1 . 1 1 1
2 1 . . . . . . . 1
6 1 1 1 . . . . . 1 1 1
4 1 . . . 1 . . . 1 . . . 1
12 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1
2 1 . . . . . . . . . . . . . . . 1
(End)
MATHEMATICA
ArrayPlot[CellularAutomaton[22, {{1}, 0}, 20]] (* N. J. A. Sloane, Aug 15 2014 *)
Total /@ CellularAutomaton[22, {{1}, 0}, 80] (* Michael De Vlieger, Oct 05 2015 *)
CROSSREFS
Cf. A071029.
Sequence in context: A129354 A129628 A245691 * A077066 A324890 A180240
KEYWORD
nonn
AUTHOR
Hans Havermann, May 26 2002
EXTENSIONS
Better description from N. J. A. Sloane, Aug 15 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)