A267812 Decimal representation of the n-th iteration of the "Rule 217" elementary cellular automaton starting with a single ON (black) cell.

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.

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 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.

Cf. A129868, A267685.

Sequence in context: A143938 A042428 A158554 * A029699 A087795 A036927

Adjacent sequences: A267809 A267810 A267811 * A267813 A267814 A267815

Keyword

nonn

Author

Robert Price, Jan 20 2016

Status

approved