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

Author

Robert Price, Jan 13 2016

Keywords

• nonn
• easy

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

Crossrefs

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

Programs

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 *)

Python

def A267367(n):
    i, s, z = n, 0, 1
    while 0 <= i: s += 1<A267367(n) for n in range(33)]) # Peter Luschny, Dec 02 2017