A266258 Number of OFF (white) cells in the n-th iteration of the "Rule 11" elementary cellular automaton starting with a single ON (black) cell.

0, 2, 3, 2, 7, 2, 11, 2, 15, 2, 19, 2, 23, 2, 27, 2, 31, 2, 35, 2, 39, 2, 43, 2, 47, 2, 51, 2, 55, 2, 59, 2, 63, 2, 67, 2, 71, 2, 75, 2, 79, 2, 83, 2, 87, 2, 91, 2, 95, 2, 99, 2, 103, 2, 107, 2, 111, 2, 115, 2, 119, 2, 123, 2, 127, 2, 131, 2, 135, 2, 139, 2

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..999

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

Conjectures from Colin Barker, Dec 27 2015 and Apr 14 2019: (Start)

a(n) = (2*(-1)^n*n+2*n-3*(-1)^n+1)/2 for n>0

a(n) = 2*a(n-2)-a(n-4) for n>4.

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

(End)

Mathematica

rule=11; 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. A266253.

Sequence in context: A262427 A333986 A349664 * A354486 A180916 A319374

Adjacent sequences: A266255 A266256 A266257 * A266259 A266260 A266261

Keyword

nonn,easy

Author

Robert Price, Dec 25 2015

Extensions

Conjectures from Colin Barker, Apr 14 2019

Status

approved