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 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 Robert Price, Table of n, a(n) for n = 0..1000 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, Illustration of first 21 generations 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 A180240 A065228 Adjacent sequences:  A071041 A071042 A071043 * A071045 A071046 A071047 KEYWORD nonn AUTHOR Hans Havermann, May 26 2002 EXTENSIONS Better description from N. J. A. Sloane, Aug 15 2014 STATUS approved

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