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A266674 Decimal representation of the n-th iteration of the "Rule 57" elementary cellular automaton starting with a single ON (black) cell. 1
1, 1, 10, 75, 76, 1623, 600, 29295, 4784, 496351, 37728, 8164799, 300736, 132422527, 2403712, 2133112575, 19192576, 34244750847, 153466368, 548835613695, 1227582464, 8788730820607, 9818265600, 140678589542399, 78541336576, 2251328604004351, 628321116160 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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 (0,27,8,-202,-216,432,1616,-256,-3456,0,2048).

FORMULA

G.f.: (1 +x -17*x^2 +40*x^3 -64*x^5 -248*x^6 +128*x^7 +1472*x^8 -2048*x^10) / ((1 -x)*(1 +x)*(1 -2*x)*(1 -4*x)*(1 +4*x)*(1 -2*x^2)*(1 +2*x +4*x^2)*(1 -8*x^2)). - Colin Barker, Jan 03 2016

MATHEMATICA

rule=57; 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 *)

PROG

(PARI) Vec((1 +x -17*x^2 +40*x^3 -64*x^5 -248*x^6 +128*x^7 +1472*x^8 -2048*x^10) / ((1 -x)*(1 +x)*(1 -2*x)*(1 -4*x)*(1 +4*x)*(1 -2*x^2)*(1 +2*x +4*x^2)*(1 -8*x^2)) + O(x^30)) \\ Colin Barker, Jan 03 2016

CROSSREFS

Cf. A266672.

Sequence in context: A103434 A119167 A233100 * A233455 A027778 A026969

Adjacent sequences:  A266671 A266672 A266673 * A266675 A266676 A266677

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 02 2016

STATUS

approved

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Last modified October 22 06:02 EDT 2018. Contains 316432 sequences. (Running on oeis4.)