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A267258 Decimal representation of the middle column of the "Rule 111" elementary cellular automaton starting with a single ON (black) cell. 1
1, 3, 7, 15, 31, 63, 127, 255, 510, 1021, 2042, 4085, 8170, 16341, 32682, 65365, 130730, 261461, 522922, 1045845, 2091690, 4183381, 8366762, 16733525, 33467050, 66934101, 133868202, 267736405, 535472810, 1070945621, 2141891242, 4283782485, 8567564970 (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

Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

FORMULA

From Colin Barker, Jan 13 2016: (Start)

a(n) = (383*2^n-32*((-1)^n+3))/192 for n>5.

G.f.: (1+x-x^8) / ((1-x)*(1+x)*(1-2*x)).

(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 *) mc=Table[catri[[k]][[k]], {k, 1, rows}]; (* Keep only middle cell from each row *) Table[FromDigits[Take[mc, k], 2], {k, 1, rows}]  (* Binary Representation of Middle Column *)

CoefficientList[Series[(1 + x - x^8)/((1 - x) (1 + x) (1 - 2 x)), {x, 0, 32}], x] (* Michael De Vlieger, Jan 13 2016 *)

PROG

(PARI) Vec((1+x-x^8)/((1-x)*(1+x)*(1-2*x)) + O(x^50)) \\ Colin Barker, Jan 13 2016

CROSSREFS

Cf. A267253.

Sequence in context: A043747 A105754 A116690 * A213247 A043755 A105755

Adjacent sequences:  A267255 A267256 A267257 * A267259 A267260 A267261

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 12 2016

STATUS

approved

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Last modified December 16 07:41 EST 2017. Contains 296076 sequences.