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A263806 Decimal representation of the n-th iteration of the "Rule 157" elementary cellular automaton starting with a single ON (black) cell. 1
1, 3, 7, 47, 95, 703, 1407, 11007, 22015, 175103, 350207, 2797567, 5595135, 44744703, 89489407, 715849727, 1431699455, 11453333503, 22906667007, 183252287487, 366504574975, 2932032405503, 5864064811007, 46912501710847, 93825003421695, 750599960264703 (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 20 2016 and Apr 17 2019: (Start)

a(n) = 3*a(n-1)+14*a(n-2)-48*a(n-3)+32*a(n-4) for n>4.

G.f.: (1-16*x^2+32*x^3-32*x^4) / ((1-x)*(1-2*x)*(1-4*x)*(1+4*x)).

(End)

MATHEMATICA

rule=157; 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. A263804.

Sequence in context: A132565 A129518 A007670 * A074714 A064457 A318087

Adjacent sequences:  A263803 A263804 A263805 * A263807 A263808 A263809

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 17 2016

STATUS

approved

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Last modified September 19 17:35 EDT 2021. Contains 347564 sequences. (Running on oeis4.)