A267154 Decimal representation of the n-th iteration of the "Rule 107" elementary cellular automaton starting with a single ON (black) cell.

1, 4, 11, 110, 119, 1978, 475, 32510, 1799, 523002, 6939, 8388350, 1799, 134216442, 6939, 2147483390, 1799, 34359737082, 6939, 549755813630, 1799, 8796093020922, 6939, 140737488355070, 1799, 2251799813683962, 6939, 36028797018963710, 1799, 576460752303422202

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 11 2016 and Apr 19 2019: (Start)

a(n) = 16*a(n-2)+a(n-4)-16*a(n-6) for n>12.

G.f.: (1+4*x-5*x^2+46*x^3-58*x^4+214*x^5-1424*x^6+816*x^7-5744*x^8 +2624*x^9 -20416*x^10 +19456*x^11 -103424*x^12) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1+x^2)).

(End)

Mathematica

rule=107; 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. A267152, A267153.

Sequence in context: A266894 A296617 A144744 * A320501 A214113 A167418

Adjacent sequences: A267151 A267152 A267153 * A267155 A267156 A267157

Keyword

nonn,easy

Author

Robert Price, Jan 11 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