A267207 Decimal representation of the n-th iteration of the "Rule 109" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 31, 34, 471, 762, 7967, 8866, 120791, 194810, 2037023, 2277026, 30918615, 49850618, 521532703, 582893218, 7914997719, 12762196218, 133512164639, 149219327650, 2026242918359, 3267120572666, 34179103454495, 38200175902370, 518718173824983

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

Empirical g.f.: (1 +4*x +39*x^2 +104*x^3 +406*x^4 +812*x^5 +1352*x^6 +1120*x^7 +256*x^8 -3584*x^10) / ((1 -x)*(1 +x)*(1 -4*x)*(1 +4*x)*(1 +x^2)*(1 +2*x +4*x^2)*(1 +16*x^2)). - Colin Barker, Jan 13 2016 and Apr 19 2019

Mathematica

rule=109; 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. A243566.

Sequence in context: A053234 A020896 A042153 * A102630 A264783 A215031

Adjacent sequences: A267204 A267205 A267206 * A267208 A267209 A267210

Keyword

nonn,easy

Author

Robert Price, Jan 11 2016

Status

approved