A267369 Total number of OFF (white) cells after n iterations of the "Rule 126" elementary cellular automaton starting with a single ON (black) cell.

0, 0, 1, 1, 6, 9, 14, 14, 27, 38, 51, 58, 75, 86, 99, 99, 128, 155, 184, 207, 240, 267, 296, 311, 352, 387, 424, 447, 488, 515, 544, 544, 605, 664, 725, 780, 845, 904, 965, 1012, 1085, 1152, 1221, 1276, 1349, 1408, 1469, 1500, 1589, 1672, 1757, 1828, 1917

Offset

0,5

References

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Links

Robert Price, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Mathematica

rule=126; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) nbc=Table[Total[catri[[k]]], {k, 1, rows}]; (* Number of Black cells in stage n *) nwc=Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}]; (* Number of White cells in stage n *) Table[Total[Take[nwc, k]], {k, 1, rows}] (* Number of White cells through stage n *)

Crossrefs

Cf. A071035.

Sequence in context: A176212 A232553 A155705 * A177891 A370125 A367947

Adjacent sequences: A267366 A267367 A267368 * A267370 A267371 A267372

Keyword

nonn,easy

Author

Robert Price, Jan 13 2016

Status

approved