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A265223
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Total number of OFF (white) cells after n iterations of the "Rule 150" elementary cellular automaton starting with a single ON (black) cell.
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1
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0, 0, 2, 4, 10, 12, 20, 24, 38, 48, 60, 68, 88, 100, 118, 128, 158, 184, 212, 236, 268, 284, 314, 328, 372, 408, 446, 476, 522, 548, 588, 608, 670, 728, 788, 844, 908, 956, 1018, 1064, 1136, 1192, 1250, 1292, 1366, 1412, 1472, 1504, 1596, 1680, 1766, 1844
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OFFSET
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0,3
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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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EXAMPLE
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First 12 rows, replacing "1" with ".", ignoring "0" outside of range of 1's for better visibility of OFF cells, followed by total number of OFF cells per row and running total up to that row:
. = 0 -> 0
. . . = 0 -> 0
. 0 . 0 . = 2 -> 2
. . 0 . 0 . . = 2 -> 4
. 0 0 0 . 0 0 0 . = 6 -> 10
. . . 0 . . . 0 . . . = 2 -> 12
. 0 . 0 0 0 . 0 0 0 . 0 . = 8 -> 20
. . 0 . . 0 . . . 0 . . 0 . . = 4 -> 24
. 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 . = 14 -> 38
. . . 0 0 0 0 0 . . . 0 0 0 0 0 . . . = 10 -> 48
. 0 . 0 . 0 0 0 . 0 . 0 . 0 0 0 . 0 . 0 . = 12 -> 60
. . 0 . 0 . . 0 . . 0 . 0 . . 0 . . 0 . 0 . . = 8 -> 68
. 0 0 0 . 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 . 0 0 0 . = 20 -> 88
(End)
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MATHEMATICA
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lim = 51; a = {}; Do[AppendTo[a, Take[#, 2 (k - 1) + 1] &@ Take[#[[k]], -(lim + k)]], {k, Length@ #}] &@ CellularAutomaton[150, {{1}, 0}, lim]; Accumulate[Count[#, n_ /; n == 0] & /@ a] (* Michael De Vlieger, Dec 09 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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