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A262864 Decimal representation of the middle column of the "Rule 147" elementary cellular automaton starting with a single ON (black) cell. 2
1, 2, 4, 9, 19, 38, 76, 153, 307, 614, 1228, 2457, 4915, 9830, 19660, 39321, 78643, 157286, 314572, 629145, 1258291, 2516582, 5033164, 10066329, 20132659, 40265318, 80530636, 161061273, 322122547, 644245094, 1288490188, 2576980377, 5153960755, 10307921510 (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

Stephen 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,-3,3,-2).

FORMULA

From Colin Barker, Jan 17 2016 and Apr 16 2019: (Start)

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

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

(End)

a(n) = floor(6*2^n/5). - Karl V. Keller, Jr., Apr 12 2021

MATHEMATICA

rule=147; 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 *) mc=Table[catri[[k]][[k]], {k, 1, rows}]; (* Keep only middle cell from each row *) Table[FromDigits[Take[mc, k], 2], {k, 1, rows}]  (* Binary Representation of Middle Column *)

PROG

(Python) print([6*2**n//5 for n in range(50)]) # Karl V. Keller, Jr., Apr 12 2021

CROSSREFS

Cf. A262808, A262863 (in binary).

Sequence in context: A081490 A292478 A309267 * A129784 A329356 A125050

Adjacent sequences:  A262861 A262862 A262863 * A262865 A262866 A262867

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 17 2016

STATUS

approved

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Last modified August 1 22:36 EDT 2021. Contains 346408 sequences. (Running on oeis4.)