A266382 Decimal representation of the n-th iteration of the "Rule 22" elementary cellular automaton starting with a single ON (black) cell.

1, 7, 17, 119, 257, 1799, 4369, 30583, 65537, 458759, 1114129, 7798903, 16843009, 117901063, 286331153, 2004318071, 4294967297, 30064771079, 73014444049, 511101108343, 1103806595329, 7726646167303, 18764712120593, 131352984844151, 281479271743489

Offset: 0

Author

Robert Price, Dec 28 2015

Keywords

• nonn
• easy

Comments

Empirical observation: This sequence can also be generated in Conway's Game of Life by setting the initial condition to be an infinite row of ON cells in both directions. After each iteration, rows of cells turned ON will be labeled as 1 and rows that are OFF will be labeled 0. When the resulting binary number is converted to decimal notation, the resulting sequence is the same as A266382. [Brook Estifanos, Mar 09 2016]

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
• A. J. Macfarlane, Generating functions for integer sequences defined by the evolution of cellular automata..., Fig. 6
• Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
• Index entries for sequences related to cellular automata
• Index to Elementary Cellular Automata

Crossrefs

Cf. A071029.

Programs

Mathematica

rule=22; rows=30; 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 *)