A266980 Decimal representation of the n-th iteration of the "Rule 79" elementary cellular automaton starting with a single ON (black) cell.

1, 6, 5, 122, 21, 2026, 85, 32682, 341, 523946, 1365, 8387242, 5461, 134212266, 21845, 2147461802, 87381, 34359650986, 349525, 549755464362, 1398101, 8796091624106, 5592405, 140737482762922, 22369621, 2251799791315626, 89478485, 36028796929485482, 357913941

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 08 2016 and Apr 18 2019: (Start)

a(n) = 21*a(n-2)-84*a(n-4)+64*a(n-6) for n>5.

G.f.: (1+6*x-16*x^2-4*x^3-32*x^5) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)).

(End)

Mathematica

rule=79; 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. A266978, A266979.

Sequence in context: A268000 A223529 A189422 * A130554 A291067 A037054

Adjacent sequences: A266977 A266978 A266979 * A266981 A266982 A266983

Keyword

nonn,easy

Author

Robert Price, Jan 07 2016

Extensions

Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - Michael De Vlieger, Jun 13 2022

Status

approved