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A266980
Decimal representation of the n-th iteration of the "Rule 79" elementary cellular automaton starting with a single ON (black) cell.
2
1, 6, 5, 122, 21, 2026, 85, 32682, 341, 523946, 1365, 8387242, 5461, 134212266, 21845, 2147461802, 87381, 34359650986, 349525, 549755464362, 1398101, 8796091624106, 5592405, 140737482762922, 22369621, 2251799791315626, 89478485, 36028796929485482, 357913941
OFFSET
0,2
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
Conjectures from Colin Barker, Jan 08 2016 and Apr 18 2019: (Start)
a(n) = 21*a(n-2)-84*a(n-4)+64*a(n-6) for n>5.
G.f.: (1+6*x-16*x^2-4*x^3-32*x^5) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)).
(End)
MATHEMATICA
rule=79; 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
Sequence in context: A268000 A223529 A189422 * A130554 A291067 A037054
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 07 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