A266251 Number of OFF (white) cells in the n-th iteration of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell.

0, 3, 3, 5, 5, 6, 9, 6, 13, 6, 17, 6, 21, 6, 25, 6, 29, 6, 33, 6, 37, 6, 41, 6, 45, 6, 49, 6, 53, 6, 57, 6, 61, 6, 65, 6, 69, 6, 73, 6, 77, 6, 81, 6, 85, 6, 89, 6, 93, 6, 97, 6, 101, 6, 105, 6, 109, 6, 113, 6, 117, 6, 121, 6, 125, 6, 129, 6, 133, 6, 137, 6

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 28 2015 and Apr 14 2019: (Start)

a(n) = (2*(-1)^n*n+2*n-9*(-1)^n+3)/2 for n>3.

a(n) = 2*a(n-2)-a(n-4) for n>7.

G.f.: x*(3+3*x-x^2-x^3-x^4+2*x^5-x^6) / ((1-x)^2*(1+x)^2).

(End)

Mathematica

rule=9; 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. A266243.

Sequence in context: A318916 A035299 A338215 * A021302 A004649 A367004

Adjacent sequences: A266248 A266249 A266250 * A266252 A266253 A266254

Keyword

nonn,easy

Author

Robert Price, Dec 25 2015

Extensions

Conjectures from Colin Barker, Apr 14 2019

Status

approved