A267367 Decimal representation of the middle column of the "Rule 126" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 6, 13, 26, 52, 104, 209, 418, 836, 1672, 3344, 6688, 13376, 26752, 53505, 107010, 214020, 428040, 856080, 1712160, 3424320, 6848640, 13697280, 27394560, 54789120, 109578240, 219156480, 438312960, 876625920, 1753251840, 3506503681, 7013007362

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

Eric Weisstein's World of Mathematics, Rule 126

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Maple

A267367 := proc(n) local i, s, z; s := 0; i := n; z := 1;
while 0 <= i do s := s+2^i; i := i-z; z := z+z od; s end:
seq(A267367(n), n=0..32); # Peter Luschny, Dec 02 2017

Mathematica

rule=126; 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)
def A267367(n):
    i, s, z = n, 0, 1
    while 0 <= i: s += 1<<i; i -= z; z += z
    return s
print([A267367(n) for n in range(33)]) # Peter Luschny, Dec 02 2017

Crossrefs

Cf. A267366 (binary), A001855, A071035, A267365.

Sequence in context: A032198 A079941 A255125 * A265385 A019300 A072762

Adjacent sequences: A267364 A267365 A267366 * A267368 A267369 A267370

Keyword

nonn,easy

Author

Robert Price, Jan 13 2016

Status

approved