A267802 Decimal representation of the n-th iteration of the "Rule 213" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 19, 115, 499, 2035, 8179, 32755, 131059, 524275, 2097139, 8388595, 33554419, 134217715, 536870899, 2147483635, 8589934579, 34359738355, 137438953459, 549755813875, 2199023255539, 8796093022195, 35184372088819, 140737488355315, 562949953421299

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 21 2016: (Start)

a(n) = 5*a(n-1)-4*a(n-2) for n>3.

G.f.: (1+2*x)*(1-4*x+16*x^2) / ((1-x)*(1-4*x)).

(End)

Conjecture: a(n) = 2^(2*n+1) - 13 for n>1. - Colin Barker, Nov 25 2016

Mathematica

rule=213; 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. A267800.

Sequence in context: A037662 A116979 A351029 * A229928 A309183 A261777

Adjacent sequences: A267799 A267800 A267801 * A267803 A267804 A267805

Keyword

nonn

Author

Robert Price, Jan 20 2016

Status

approved