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A266839
Decimal representation of the n-th iteration of the "Rule 67" elementary cellular automaton starting with a single ON (black) cell.
3
1, 4, 10, 97, 92, 1803, 736, 30815, 5888, 508671, 47104, 8263679, 376832, 133218303, 3014656, 2139488255, 24117248, 34295775231, 192937984, 549244108799, 1543503872, 8791999381503, 12348030976, 140704739229695, 98784247808, 2251537820680191, 790273982464
OFFSET
0,2
FORMULA
Conjectures from Colin Barker, Jan 05 2016 and Apr 18 2019: (Start)
a(n) = 25*a(n-2) - 152*a(n-4) + 128*a(n-6) for n > 9.
G.f.: (1 + 4*x - 15*x^2 - 3*x^3 - 6*x^4 - 14*x^5 - 172*x^6 - 28*x^7 + 192*x^8 - 64*x^9) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-8*x^2)).
(End)
Conjecture: a(n) = 2*4^n - 61*8^floor(n/2)/16 - 1 for odd n > 2; a(n) = 23*8^(n/2)/16 for even n > 3. - Karl V. Keller, Jr., Dec 16 2021
MATHEMATICA
rule=67; 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: A059919 A143047 A156329 * A203179 A125855 A261842
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 04 2016
STATUS
approved