A267158 Number of ON (black) cells in the n-th iteration of the "Rule 107" elementary cellular automaton starting with a single ON (black) cell.

1, 1, 3, 5, 6, 8, 7, 13, 6, 15, 8, 21, 6, 23, 8, 29, 6, 31, 8, 37, 6, 39, 8, 45, 6, 47, 8, 53, 6, 55, 8, 61, 6, 63, 8, 69, 6, 71, 8, 77, 6, 79, 8, 85, 6, 87, 8, 93, 6, 95, 8, 101, 6, 103, 8, 109, 6, 111, 8, 117, 6, 119, 8, 125, 6, 127, 8, 133, 6, 135, 8, 141

Offset

0,3

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-2)+a(n-4)-a(n-6) 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)^2*(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 *) Table[Total[catri[[k]]], {k, 1, rows}] (* Number of Black cells in stage n *)

Crossrefs

Cf. A267152.

Sequence in context: A337092 A021741 A201906 * A161529 A133043 A094058

Adjacent sequences: A267155 A267156 A267157 * A267159 A267160 A267161

Keyword

nonn,easy

Author

Robert Price, Jan 11 2016

Status

approved