A267527 Decimal representation of the n-th iteration of the "Rule 141" elementary cellular automaton starting with a single ON (black) cell.

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

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

Formula

From Colin Barker, Jan 16 2016 and Apr 19 2019: (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)

a(n) = 2^n*(4^floor(n/2) - 1)/3 + 2^(n-1) - 1 for n > 1. - Karl V. Keller, Jr., Sep 22 2021

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

(Python) print([1, 2] + [2**n*(4**(n//2) - 1)//3 + 2**(n-1) - 1 for n in range(2, 50)]) # Karl V. Keller, Jr., Sep 22 2021

Crossrefs

Cf. A267525, A267526.

Sequence in context: A262228 A362351 A213073 * A286453 A309375 A018847

Adjacent sequences: A267524 A267525 A267526 * A267528 A267529 A267530

Keyword

nonn,easy

Author

Robert Price, Jan 16 2016

Status

approved