A262864 Decimal representation of the middle column of the "Rule 147" elementary cellular automaton starting with a single ON (black) cell.

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

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