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A267812
Decimal representation of the n-th iteration of the "Rule 217" elementary cellular automaton starting with a single ON (black) cell.
1
1, 1, 27, 119, 495, 2015, 8127, 32639, 130815, 523775, 2096127, 8386559, 33550335, 134209535, 536854527, 2147450879, 8589869055, 34359607295, 137438691327, 549755289599, 2199022206975, 8796090925055, 35184367894527, 140737479966719, 562949936644095
OFFSET
0,3
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
Conjectures from Colin Barker, Jan 22 2016: (Start)
a(n) = 7*a(n-1)-14*a(n-2)+8*a(n-3) for n>4.
G.f.: (1-6*x+34*x^2-64*x^3+32*x^4) / ((1-x)*(1-2*x)*(1-4*x)).
(End)
MATHEMATICA
rule=217; 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. A267810.
Sequence in context: A143938 A042428 A158554 * A029699 A087795 A036927
KEYWORD
nonn
AUTHOR
Robert Price, Jan 20 2016
STATUS
approved