A263806 Decimal representation of the n-th iteration of the "Rule 157" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 7, 47, 95, 703, 1407, 11007, 22015, 175103, 350207, 2797567, 5595135, 44744703, 89489407, 715849727, 1431699455, 11453333503, 22906667007, 183252287487, 366504574975, 2932032405503, 5864064811007, 46912501710847, 93825003421695, 750599960264703

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 20 2016 and Apr 17 2019: (Start)

a(n) = 3*a(n-1)+14*a(n-2)-48*a(n-3)+32*a(n-4) for n>4.

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

(End)

Mathematica

rule=157; 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 *)

Prog

(

Crossrefs

Cf. A263804, A263805.

Sequence in context: A132565 A129518 A007670 * A074714 A064457 A318087

Adjacent sequences: A263803 A263804 A263805 * A263807 A263808 A263809

Keyword

nonn,easy

Author

Robert Price, Jan 17 2016

Status

approved