A266461 Decimal representation of the n-th iteration of the "Rule 27" elementary cellular automaton starting with a single ON (black) cell.

1, 5, 2, 123, 4, 2039, 8, 32751, 16, 524255, 32, 8388543, 64, 134217599, 128, 2147483391, 256, 34359737855, 512, 549755812863, 1024, 8796093020159, 2048, 140737488351231, 4096, 2251799813677055, 8192, 36028797018947583, 16384, 576460752303390719, 32768

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, Dec 31 2015 and Apr 16 2019: (Start)

a(n) = 19*a(n-2)-50*a(n-4)+32*a(n-6) for n>5.

G.f.: (1+5*x-17*x^2+28*x^3+16*x^4-48*x^5) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-2*x^2)).

(End)

Conjecture: a(n) = 2*(4^n - 2^floor(n/2)) - 1 for odd n; a(n) = 2^(n/2) for even n. - Karl V. Keller, Jr., Sep 29 2021

Mathematica

rule=27; 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. A266459, A266460.

Sequence in context: A099612 A233044 A142599 * A068566 A347426 A212481

Adjacent sequences: A266458 A266459 A266460 * A266462 A266463 A266464

Keyword

nonn,easy

Author

Robert Price, Dec 29 2015

Status

approved