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A266976 Decimal representation of the n-th iteration of the "Rule 78" elementary cellular automaton starting with a single ON (black) cell. 1
1, 6, 28, 104, 464, 1696, 7488, 27264, 120064, 436736, 1922048, 6989824, 30756864, 111845376, 492126208, 1789558784, 7874084864, 28633071616, 125985619968, 458129670144, 2015770968064, 7330076819456, 32252339683328, 117281237499904, 516037451710464 (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 08 2016 and Apr 18 2019: (Start)

a(n) = 2^(n-2)*((-2)^n+21*2^n-4)/3 for n>0.

a(n) = 2*a(n-1)+16*a(n-2)-32*a(n-3) for n>3.

G.f.: (1+4*x-16*x^3) / ((1-2*x)*(1-4*x)*(1+4*x)).

(End)

MATHEMATICA

rule=78; 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 *) Table[FromDigits[catri[[k]], 2], {k, 1, rows}]   (* Decimal Representation of Rows *)

CROSSREFS

Cf. A266974.

Sequence in context: A011856 A276041 A134416 * A117999 A234617 A028379

Adjacent sequences:  A266973 A266974 A266975 * A266977 A266978 A266979

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 07 2016

STATUS

approved

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Last modified June 25 05:41 EDT 2019. Contains 324346 sequences. (Running on oeis4.)