A266248 Decimal representation of the middle column of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 5, 10, 21, 43, 86, 173, 346, 693, 1386, 2773, 5546, 11093, 22186, 44373, 88746, 177493, 354986, 709973, 1419946, 2839893, 5679786, 11359573, 22719146, 45438293, 90876586, 181753173, 363506346, 727012693, 1454025386, 2908050773, 5816101546, 11632203093

Offset

0,2

References

Stephen 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

Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

Formula

From Colin Barker, Dec 28 2015 and Apr 14 2019: (Start)

a(n) = (65*2^n-8*((-1)^n+3))/48 for n>3.

a(n) = 2*a(n-1)+a(n-2)-2*a(n-3) for n>6.

G.f.: (1+x^5-x^6) / ((1-x)*(1+x)*(1-2*x)).

(End)

a(n) = floor(65*2^n/48). - Karl V. Keller, Jr., Dec 15 2021

Mathematica

rule=9; 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([65*2**n//48 for n in range(50)]) # Karl V. Keller, Jr., Dec 15 2021

Crossrefs

Cf. A266243, A266247.

Sequence in context: A352875 A245747 A032283 * A027437 A267444 A267880

Adjacent sequences: A266245 A266246 A266247 * A266249 A266250 A266251

Keyword

nonn,easy

Author

Robert Price, Dec 25 2015

Status

approved