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A266284 Decimal representation of the n-th iteration of the "Rule 13" elementary cellular automaton starting with a single ON (black) cell. 1
1, 2, 5, 106, 21, 1962, 85, 32426, 341, 522922, 1365, 8383146, 5461, 134195882, 21845, 2147396266, 87381, 34359388842, 349525, 549754415786, 1398101, 8796087429802, 5592405, 140737465985706, 22369621, 2251799724206762, 89478485, 36028796661050026, 357913941 (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..999

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

FORMULA

Conjectures from Colin Barker, Dec 27 2015 and Apr 14 2019: (Start)

a(n) = 21*a(n-2)-84*a(n-4)+64*a(n-6) for n>5.

G.f.: (1+2*x-16*x^2+64*x^3-96*x^5) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)).

(End)

MATHEMATICA

rule=13; 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. A266282.

Sequence in context: A136106 A122696 A237267 * A215572 A023263 A070855

Adjacent sequences:  A266281 A266282 A266283 * A266285 A266286 A266287

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 26 2015

EXTENSIONS

Conjectures from Colin Barker, Apr 14 2019

STATUS

approved

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Last modified May 27 20:48 EDT 2020. Contains 334667 sequences. (Running on oeis4.)