A267139 Decimal representation of the n-th iteration of the "Rule 103" elementary cellular automaton starting with a single ON (black) cell.

1, 6, 6, 117, 60, 1931, 376, 32535, 752, 523823, 1504, 8387679, 3008, 134215871, 6016, 2147479935, 12032, 34359730943, 24064, 549755799039, 48128, 8796092992511, 96256, 140737488295935, 192512, 2251799813566463, 385024, 36028797018726399, 770048

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 11 2016 and Apr 19 2019: (Start)

a(n) = 19*a(n-2) - 50*a(n-4) + 32*a(n-6) for n > 10.

G.f.: (1 + 6*x - 13*x^2 + 3*x^3 - 4*x^4 + 8*x^5 - 496*x^6 + 1504*x^7 - 3584*x^8 - 1536*x^9 + 4096*x^10) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-2*x^2)). (End)

Mathematica

rule=103; 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. A267136, A267138.

Sequence in context: A320824 A085804 A012125 * A170915 A328186 A123190

Adjacent sequences: A267136 A267137 A267138 * A267140 A267141 A267142

Keyword

nonn,easy

Author

Robert Price, Jan 10 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