A267006 Triangle read by rows giving successive states of cellular automaton generated by "Rule 84" initiated with a single ON (black) cell.

1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0

Offset

0

Comments

Row n has length 2n+1.

This sequence is also generated by Rules 116, 212 and 244.

References

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Links

Robert Price, Table of n, a(n) for n = 0..10000

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

Example

The first ten rows:
                  1
                0 1 1
              0 0 0 1 1
            0 0 0 0 0 1 1
          0 0 0 0 0 0 0 1 1
        0 0 0 0 0 0 0 0 0 1 1
      0 0 0 0 0 0 0 0 0 0 0 1 1
    0 0 0 0 0 0 0 0 0 0 0 0 0 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1

Maple

seq(abs( floor(sqrt(n+2)) - 2*floor(sqrt(n+1)) + floor(sqrt(n)) ), n = 0..100); # Peter Bala, Apr 08 2017

Mathematica

rule=84; 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 *) Flatten[catri] (* Triangle Representation of CA *)

Prog

(PARI) for(n=0, 100, print1(abs(sqrtint(n + 2) - 2*sqrtint(n + 1) + sqrtint(n)), ", ")) \\ Indranil Ghosh, Apr 08 2017

Crossrefs

Cf. A266298.

Sequence in context: A275973 A218173 A068426 * A280816 A265246 A138709

Adjacent sequences: A267003 A267004 A267005 * A267007 A267008 A267009

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 08 2016

Status

approved