A266616 Number of OFF (white) cells in the n-th iteration of the "Rule 41" elementary cellular automaton starting with a single ON (black) cell.

0, 3, 3, 4, 8, 3, 11, 4, 16, 3, 19, 4, 24, 3, 27, 4, 32, 3, 35, 4, 40, 3, 43, 4, 48, 3, 51, 4, 56, 3, 59, 4, 64, 3, 67, 4, 72, 3, 75, 4, 80, 3, 83, 4, 88, 3, 91, 4, 96, 3, 99, 4, 104, 3, 107, 4, 112, 3, 115, 4, 120, 3, 123, 4, 128, 3, 131, 4, 136, 3, 139, 4

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 02 2016 and Apr 18 2019: (Start)

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

G.f.: x*(3+3*x+x^2+5*x^3-4*x^4) / ((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 *) nbc=Table[Total[catri[[k]]], {k, 1, rows}]; (* Number of Black cells in stage n *) Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}] (* Number of White cells in stage n *)

Crossrefs

Cf. A266608.

Sequence in context: A246023 A049927 A329216 * A360846 A340429 A147679

Adjacent sequences: A266613 A266614 A266615 * A266617 A266618 A266619

Keyword

nonn

Author

Robert Price, Jan 01 2016

Status

approved