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A266287 Total number of OFF (white) cells after n iterations of the "Rule 13" elementary cellular automaton starting with a single ON (black) cell. 1
0, 2, 5, 8, 14, 18, 27, 32, 44, 50, 65, 72, 90, 98, 119, 128, 152, 162, 189, 200, 230, 242, 275, 288, 324, 338, 377, 392, 434, 450, 495, 512, 560, 578, 629, 648, 702, 722, 779, 800, 860, 882, 945, 968, 1034, 1058, 1127, 1152, 1224, 1250, 1325, 1352, 1430 (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..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*n^2+5*n+(-1)^n*(n-1)+1)/4.

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

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

(End)

MATHEMATICA

rule=13; 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. A266282.

Sequence in context: A191109 A190105 A295400 * A111711 A095348 A215725

Adjacent sequences:  A266284 A266285 A266286 * A266288 A266289 A266290

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 26 2015

EXTENSIONS

Conjectures from Colin Barker, Apr 14 2019

STATUS

approved

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Last modified October 6 12:00 EDT 2022. Contains 357264 sequences. (Running on oeis4.)