A267159 Total number of ON (black) cells after n iterations of the "Rule 107" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 5, 10, 16, 24, 31, 44, 50, 65, 73, 94, 100, 123, 131, 160, 166, 197, 205, 242, 248, 287, 295, 340, 346, 393, 401, 454, 460, 515, 523, 584, 590, 653, 661, 730, 736, 807, 815, 892, 898, 977, 985, 1070, 1076, 1163, 1171, 1264, 1270, 1365, 1373, 1474, 1480

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 11 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.: (1+x+2*x^2+4*x^3+2*x^4+2*x^5-x^6+x^7-4*x^8-x^9+x^10+x^11-x^12) / ((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 *) Table[Total[Take[nbc, k]], {k, 1, rows}] (* Number of Black cells through stage n *)

Crossrefs

Cf. A267152.

Sequence in context: A131938 A031871 A026056 * A084587 A001859 A011903

Adjacent sequences: A267156 A267157 A267158 * A267160 A267161 A267162

Keyword

nonn,easy

Author

Robert Price, Jan 11 2016

Status

approved