A267161 Total number of OFF (white) cells after n iterations of the "Rule 107" elementary cellular automaton starting with a single ON (black) cell.

0, 2, 4, 6, 9, 12, 18, 20, 31, 35, 48, 50, 69, 73, 94, 96, 123, 127, 156, 158, 193, 197, 234, 236, 279, 283, 328, 330, 381, 385, 438, 440, 499, 503, 564, 566, 633, 637, 706, 708, 783, 787, 864, 866, 949, 953, 1038, 1040, 1131, 1135, 1228, 1230, 1329, 1333

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

Formula

Conjectures from Colin Barker, Jan 12 2016 and Apr 19 2019: (Start)

a(n) = a(n-1)+a(n-2)-a(n-3)+a(n-4)-a(n-5)-a(n-6)+a(n-7) for n>12.

G.f.: x*(2+2*x+x^3-x^4+x^5-x^6+4*x^7+x^8-x^9-x^10+x^11) / ((1-x)^3*(1+x)^2*(1+x^2)).

(End)

Mathematica

rule=107; 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. A267152.

Sequence in context: A238374 A133041 A079492 * A173784 A094660 A005690

Adjacent sequences: A267158 A267159 A267160 * A267162 A267163 A267164

Keyword

nonn,easy

Author

Robert Price, Jan 11 2016

Status

approved