A267519 Total number of OFF (white) cells after n iterations of the "Rule 137" elementary cellular automaton starting with a single ON (black) cell.

0, 3, 6, 11, 14, 19, 25, 33, 38, 44, 52, 60, 68, 79, 90, 103, 112, 123, 134, 147, 161, 177, 191, 205, 218, 231, 248, 270, 290, 306, 323, 347, 366, 380, 399, 424, 442, 462, 487, 511, 530, 554, 585, 612, 638, 662, 684, 716, 747, 775, 799, 828, 862, 892, 923

Offset

0,2

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=137; 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. A267463.

Sequence in context: A189380 A047398 A047924 * A200182 A342173 A282277

Adjacent sequences: A267516 A267517 A267518 * A267520 A267521 A267522

Keyword

nonn,easy

Author

Robert Price, Jan 16 2016

Status

approved