A266252 Total number of OFF (white) cells after n iterations of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell.

0, 3, 6, 11, 16, 22, 31, 37, 50, 56, 73, 79, 100, 106, 131, 137, 166, 172, 205, 211, 248, 254, 295, 301, 346, 352, 401, 407, 460, 466, 523, 529, 590, 596, 661, 667, 736, 742, 815, 821, 898, 904, 985, 991, 1076, 1082, 1171, 1177, 1270, 1276, 1373, 1379, 1480

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) = ((-1)^n*(n-4)+n*(n+4))/2 for n>2.

a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>7.

G.f.: x*(3+3*x-x^2-x^3-x^4+2*x^5-x^6) / ((1-x)^3*(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 *) nwc=Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}]; (* Number of White cells in stage n *) Table[Total[Take[nwc, k]], {k, 1, rows}] (* Number of White cells through stage n *)

Crossrefs

Cf. A266243.

Sequence in context: A366471 A024401 A333709 * A267260 A116940 A278100

Adjacent sequences: A266249 A266250 A266251 * A266253 A266254 A266255

Keyword

nonn,easy

Author

Robert Price, Dec 25 2015

Extensions

Conjectures from Colin Barker, Apr 14 2019

Status

approved