A266249 Number of ON (black) cells in the n-th iteration of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell.

1, 0, 2, 2, 4, 5, 4, 9, 4, 13, 4, 17, 4, 21, 4, 25, 4, 29, 4, 33, 4, 37, 4, 41, 4, 45, 4, 49, 4, 53, 4, 57, 4, 61, 4, 65, 4, 69, 4, 73, 4, 77, 4, 81, 4, 85, 4, 89, 4, 93, 4, 97, 4, 101, 4, 105, 4, 109, 4, 113, 4, 117, 4, 121, 4, 125, 4, 129, 4, 133, 4, 137

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..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-1)/2 for n>3.

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

G.f.: (1+2*x^3+x^4+x^5-2*x^6+x^7) / ((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 *) Table[Total[catri[[k]]], {k, 1, rows}] (* Number of Black cells in stage n *)

Crossrefs

Cf. A266243.

Sequence in context: A341867 A252938 A229402 * A276299 A231302 A231363

Adjacent sequences: A266246 A266247 A266248 * A266250 A266251 A266252

Keyword

nonn,easy

Author

Robert Price, Dec 25 2015

Extensions

Conjectures from Colin Barker, Apr 14 2019

Status

approved