A266614 Number of ON (black) cells in the n-th iteration of the "Rule 41" elementary cellular automaton starting with a single ON (black) cell.

1, 0, 2, 3, 1, 8, 2, 11, 1, 16, 2, 19, 1, 24, 2, 27, 1, 32, 2, 35, 1, 40, 2, 43, 1, 48, 2, 51, 1, 56, 2, 59, 1, 64, 2, 67, 1, 72, 2, 75, 1, 80, 2, 83, 1, 88, 2, 91, 1, 96, 2, 99, 1, 104, 2, 107, 1, 112, 2, 115, 1, 120, 2, 123, 1, 128, 2, 131, 1, 136, 2, 139

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 02 2016 and Apr 18 2019: (Start)

a(n) = a(n-2)+a(n-4)-a(n-6) for n>5.

G.f.: (1+x^2+3*x^3-2*x^4+5*x^5) / ((1-x)^2*(1+x)^2*(1+x^2)).

(End)

Mathematica

rule=41; 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. A266608.

Sequence in context: A109198 A081320 A147865 * A175314 A331123 A182223

Adjacent sequences: A266611 A266612 A266613 * A266615 A266616 A266617

Keyword

nonn,easy

Author

Robert Price, Jan 01 2016

Status

approved