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A071044
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Number of ON cells at generation n of 1-D CA defined by Rule 22, starting with a single ON cell.
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3
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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
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OFFSET
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0,2
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COMMENTS
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Number of 1's in n-th row of triangle in A071029.
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.
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LINKS
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FORMULA
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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
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EXAMPLE
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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)
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MATHEMATICA
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ArrayPlot[CellularAutomaton[22, {{1}, 0}, 20]] (* N. J. A. Sloane, Aug 15 2014 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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