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A266070
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Middle column of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell.
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6
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1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1
(list;
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OFFSET
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0
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COMMENTS
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The binomial transform is 1, 1, 1, 2, 5, 12, 27,..., i.e., A000325 with another 1 in front. The inverse binomial transform is 1, -1, 1, 0, -3, 10, -25, 56, -119, 246, -501, 1012,... essentially A000247. R. J. Mathar, Feb 16 2023
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
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LINKS
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FORMULA
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EXAMPLE
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First 8 rows at right, the center column values in parentheses are the values of the terms of this sequence at left:
a(1) (1)
a(2) 1 (0) 0
a(3) 0 0 (0) 1 0
a(4) 1 1 1 (1) 0 0 1
a(5) 0 0 0 0 (0) 0 1 0 0
a(6) 1 1 1 1 1 (1) 1 0 0 1 1
a(7) 0 0 0 0 0 0 (0) 0 0 1 0 0 0
a(8) 1 1 1 1 1 1 1 (1) 1 1 0 0 1 1 1
(End)
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MATHEMATICA
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Table[SeriesCoefficient[(-1 + x^2 - x^3)/(-1 + x^2), {x, 0, n}], {n, 0, 120}] (* Michael De Vlieger, Dec 21 2015 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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