A267689 Decimal representation of the n-th iteration of the "Rule 199" elementary cellular automaton starting with a single ON (black) cell.

1, 6, 28, 122, 500, 2026, 8148, 32682, 130900, 523946, 2096468, 8387242, 33551700, 134212266, 536859988, 2147461802, 8589890900, 34359650986, 137438778708, 549755464362, 2199022556500, 8796091624106, 35184369292628, 140737482762922, 562949942236500

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

Conjectures from Colin Barker, Jan 19 2016 and Apr 20 2019: (Start)

a(n) = 6*a(n-1) - 7*a(n-2) - 6*a(n-3) + 8*a(n-4) for n > 4.

G.f.: (1+2*x)*(1 - 2*x + 3*x^2 - 4*x^3) / ((1-x)*(1+x)*(1-2*x)*(1-4*x)).

(End)

Empirical a(n) = -1 -(-1)^n/3 - 2^(1+n)/3 + 2^(1+2*n) for n > 0. - Colin Barker, Feb 14 2017 and Apr 20 2019

Mathematica

rule=199; 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 *)

Crossrefs

Cf. A267687, A267688.

Sequence in context: A292485 A225417 A026851 * A300996 A181337 A002693

Adjacent sequences: A267686 A267687 A267688 * A267690 A267691 A267692

Keyword

nonn,easy

Author

Robert Price, Jan 19 2016

Status

approved