A267685 Decimal representation of the n-th iteration of the "Rule 203" elementary cellular automaton starting with a single ON (black) cell.

1, 4, 27, 119, 495, 2015, 8127, 32639, 130815, 523775, 2096127, 8386559, 33550335, 134209535, 536854527, 2147450879, 8589869055, 34359607295, 137438691327, 549755289599, 2199022206975, 8796090925055, 35184367894527, 140737479966719, 562949936644095

Offset

0,2

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 19 2016 and Apr 17 2019: (Start)

a(n) = 7*a(n-1)-14*a(n-2)+8*a(n-3) for n>4.

G.f.: (1-3*x+13*x^2-22*x^3+8*x^4) / ((1-x)*(1-2*x)*(1-4*x)).

(End)

a(n) = A129868(n) for n >= 2. - Georg Fischer, Mar 26 2019

a(n) = 2*4^n - 2^n - 1 for n > 1. - Karl V. Keller, Jr., Jun 07 2022

Mathematica

rule=203; 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 *)

Prog

(Python) print([1, 4]+[2*4**n - 2**n - 1 for n in range(2, 50)]) # Karl V. Keller, Jr., Jun 07 2022

Crossrefs

Cf. A129868, A267683, A267684.

Sequence in context: A156223 A048102 A171469 * A190584 A268598 A267886

Adjacent sequences: A267682 A267683 A267684 * A267686 A267687 A267688

Keyword

nonn,easy

Author

Robert Price, Jan 19 2016

Status

approved