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A267454 Total number of OFF (white) cells after n iterations of the "Rule 131" elementary cellular automaton starting with a single ON (black) cell. 1
0, 2, 5, 10, 15, 23, 30, 40, 51, 63, 75, 91, 106, 123, 141, 161, 181, 204, 226, 251, 277, 304, 331, 362, 392, 424, 457, 492, 527, 565, 602, 642, 683, 725, 767, 813, 858, 905, 953, 1003, 1053, 1106, 1158, 1213, 1269, 1326, 1383, 1444, 1504, 1566, 1629, 1694 (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 15 2016 and Apr 19 2019: (Start)

a(n) = a(n-1)+a(n-3)-a(n-5)-a(n-7)+a(n-8) for n>7.

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

(End)

MATHEMATICA

rule=131; 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. A267418.

Sequence in context: A179207 A008822 A013927 * A163059 A099738 A064513

Adjacent sequences:  A267451 A267452 A267453 * A267455 A267456 A267457

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 15 2016

STATUS

approved

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Last modified August 21 22:32 EDT 2019. Contains 326169 sequences. (Running on oeis4.)