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A267260 Total number of ON (black) cells after n iterations of the "Rule 111" elementary cellular automaton starting with a single ON (black) cell. 1
1, 3, 6, 11, 16, 23, 29, 40, 46, 61, 67, 86, 92, 115, 121, 148, 154, 185, 191, 226, 232, 271, 277, 320, 326, 373, 379, 430, 436, 491, 497, 556, 562, 625, 631, 698, 704, 775, 781, 856, 862, 941, 947, 1030, 1036, 1123, 1129, 1220, 1226, 1321, 1327, 1426, 1432 (list; graph; refs; listen; history; text; internal format)
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..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 13 2016 and Apr 19 2019: (Start)

a(n) = (n^2-((-1)^n-4)*n+4*(-1)^n)/2 for n>3.

G.f.: (1+2*x+x^2+x^3-x^5-x^6+2*x^7-x^8) / ((1-x)^3*(1+x)^2).

(End)

MATHEMATICA

rule=111; 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. A267253.

Sequence in context: A024401 A333709 A266252 * A116940 A278100 A087099

Adjacent sequences:  A267257 A267258 A267259 * A267261 A267262 A267263

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 12 2016

STATUS

approved

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Last modified May 26 18:08 EDT 2020. Contains 334630 sequences. (Running on oeis4.)