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A267882 Total number of ON (black) cells after n iterations of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell. 1
1, 1, 4, 10, 19, 30, 43, 58, 75, 94, 115, 138, 163, 190, 219, 250, 283, 318, 355, 394, 435, 478, 523, 570, 619, 670, 723, 778, 835, 894, 955, 1018, 1083, 1150, 1219, 1290, 1363, 1438, 1515, 1594, 1675, 1758, 1843, 1930, 2019, 2110, 2203, 2298, 2395, 2494 (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..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

FORMULA

Conjectures from Colin Barker, Jan 22 2016 and Apr 20 2019: (Start)

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

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

(End)

MATHEMATICA

rule=233; 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. A267868.

Sequence in context: A062198 A050858 A173248 * A238705 A022785 A241239

Adjacent sequences:  A267879 A267880 A267881 * A267883 A267884 A267885

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 21 2016

STATUS

approved

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Last modified May 25 02:01 EDT 2020. Contains 334581 sequences. (Running on oeis4.)