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A267527 Decimal representation of the n-th iteration of the "Rule 141" elementary cellular automaton starting with a single ON (black) cell. 1
1, 2, 5, 11, 87, 175, 1375, 2751, 21887, 43775, 349695, 699391, 5593087, 11186175, 89481215, 178962431, 1431666687, 2863333375, 22906535935, 45813071871, 366504050687, 733008101375, 5864062713855, 11728125427711, 93824995033087, 187649990066175 (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 (3,14,-48,32).

FORMULA

From Colin Barker, Jan 16 2016: (Start)

a(n) = 3*a(n-1)+14*a(n-2)-48*a(n-3)+32*a(n-4) for n>5.

G.f.: (1-x-15*x^2+16*x^3+48*x^4-64*x^5) / ((1-x)*(1-2*x)*(1-4*x)*(1+4*x)).

(End)

MATHEMATICA

rule=141; 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-15*x^2+16*x^3+48*x^4-64*x^5)/((1-x)*(1-2*x)*(1-4*x)*(1+4*x)) + O(x^30)) \\ Colin Barker, Jan 16 2016

CROSSREFS

Cf. A267525.

Sequence in context: A131480 A262228 A213073 * A286453 A018847 A178318

Adjacent sequences:  A267524 A267525 A267526 * A267528 A267529 A267530

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 16 2016

STATUS

approved

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Last modified February 19 16:56 EST 2018. Contains 299356 sequences. (Running on oeis4.)