A266976 Decimal representation of the n-th iteration of the "Rule 78" elementary cellular automaton starting with a single ON (black) cell.

1, 6, 28, 104, 464, 1696, 7488, 27264, 120064, 436736, 1922048, 6989824, 30756864, 111845376, 492126208, 1789558784, 7874084864, 28633071616, 125985619968, 458129670144, 2015770968064, 7330076819456, 32252339683328, 117281237499904, 516037451710464

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 08 2016 and Apr 18 2019: (Start)

a(n) = 2^(n-2)*((-2)^n+21*2^n-4)/3 = 2^(n-1)*A277954(n+1) for n>0.

a(n) = 2*a(n-1) + 16*a(n-2) - 32*a(n-3) for n>3.

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

(End)

Mathematica

rule=78; 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. A266974, A266975.

Sequence in context: A011856 A276041 A134416 * A352739 A117999 A234617

Adjacent sequences: A266973 A266974 A266975 * A266977 A266978 A266979

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