A266255 Decimal representation of the n-th iteration of the "Rule 11" elementary cellular automaton starting with a single ON (black) cell.

1, 4, 3, 124, 3, 2044, 3, 32764, 3, 524284, 3, 8388604, 3, 134217724, 3, 2147483644, 3, 34359738364, 3, 549755813884, 3, 8796093022204, 3, 140737488355324, 3, 2251799813685244, 3, 36028797018963964, 3, 576460752303423484, 3, 9223372036854775804, 3

Offset

0,2

Comments

Rule 43 also generates this sequence.

References

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

Links

Robert Price, Table of n, a(n) for n = 0..999

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

From Colin Barker, Dec 27 2015 and Apr 14 2019: (Start)

a(n) = (7*(-1)^n+2^(2*n+1)-(-1)^n*2^(2*n+1)-1)/2 for n>0.

a(n) = 17*a(n-2)-16*a(n-4) for n>4.

G.f.: (1+4*x-14*x^2+56*x^3-32*x^4) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).

(End)

a(n) = 2*4^n - 4 for odd n; a(n) = 3 - 2*0^n for even n. - Karl V. Keller, Jr., Aug 26 2021

Mathematica

rule=11; 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 *)

Prog

(Python) print([2*4**n - 4 if n%2 else 3 - 2*0**n for n in range(33)]) # Karl V. Keller, Jr., Aug 26 2021

Crossrefs

Cf. A266253, A266254, A266070, A266071, A081253, A266256, A266257, A266258, A266259.

Sequence in context: A300026 A349589 A362736 * A351792 A362674 A325871

Adjacent sequences: A266252 A266253 A266254 * A266256 A266257 A266258

Keyword

nonn,easy

Author

Robert Price, Dec 25 2015

Status

approved