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A266250 Total number of ON (black) cells after n iterations of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell. 1
1, 1, 3, 5, 9, 14, 18, 27, 31, 44, 48, 65, 69, 90, 94, 119, 123, 152, 156, 189, 193, 230, 234, 275, 279, 324, 328, 377, 381, 434, 438, 495, 499, 560, 564, 629, 633, 702, 706, 779, 783, 860, 864, 945, 949, 1034, 1038, 1127, 1131, 1224, 1228, 1325, 1329, 1430 (list; graph; refs; listen; history; text; internal format)
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) = (n^2-(-1)^n*(n-4)+2)/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.: (1+2*x^3+x^4+x^5-2*x^6+x^7) / ((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 *) Table[Total[Take[nbc, k]], {k, 1, rows}] (* Number of Black cells through stage n *)

CROSSREFS

Cf. A266243.

Sequence in context: A211389 A288259 A082874 * A127720 A118002 A069533

Adjacent sequences:  A266247 A266248 A266249 * A266251 A266252 A266253

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 25 2015

EXTENSIONS

Conjectures from Colin Barker, Apr 14 2019

STATUS

approved

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Last modified June 15 17:43 EDT 2019. Contains 324142 sequences. (Running on oeis4.)