A266839 Decimal representation of the n-th iteration of the "Rule 67" elementary cellular automaton starting with a single ON (black) cell.

1, 4, 10, 97, 92, 1803, 736, 30815, 5888, 508671, 47104, 8263679, 376832, 133218303, 3014656, 2139488255, 24117248, 34295775231, 192937984, 549244108799, 1543503872, 8791999381503, 12348030976, 140704739229695, 98784247808, 2251537820680191, 790273982464

Offset

0,2

Links

Robert Price, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

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

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

Conjectures from Colin Barker, Jan 05 2016 and Apr 18 2019: (Start)

a(n) = 25*a(n-2) - 152*a(n-4) + 128*a(n-6) for n > 9.

G.f.: (1 + 4*x - 15*x^2 - 3*x^3 - 6*x^4 - 14*x^5 - 172*x^6 - 28*x^7 + 192*x^8 - 64*x^9) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-8*x^2)).

(End)

Conjecture: a(n) = 2*4^n - 61*8^floor(n/2)/16 - 1 for odd n > 2; a(n) = 23*8^(n/2)/16 for even n > 3. - Karl V. Keller, Jr., Dec 16 2021

Mathematica

rule=67; 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. A266837, A266838.

Sequence in context: A059919 A143047 A156329 * A203179 A125855 A261842

Adjacent sequences: A266836 A266837 A266838 * A266840 A266841 A266842

Keyword

nonn,easy

Author

Robert Price, Jan 04 2016

Status

approved