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A267154 Decimal representation of the n-th iteration of the "Rule 107" elementary cellular automaton starting with a single ON (black) cell. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 10 10:09 EDT 2022. Contains 356039 sequences. (Running on oeis4.)