0,2

Rule 156 also generates this sequence.

Also, the binary representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 678", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. See A283641.

Robert Price, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Index entries for linear recurrences with constant coefficients, signature (10,1,-10).

From Colin Barker, Dec 30 2015 and Apr 16 2019: (Start)

a(n) = (44 - 45*(-1)^n + 10^(2+n))/99.

a(n) = 10*a(n-1) + a(n-2) - 10*a(n-3) for n>2.

G.f.: (1+x-10*x^2) / ((1-x)*(1+x)*(1-10*x)).

(End)

a(n) = floor((100*10^n + 89)/99). - Karl V. Keller, Jr., Sep 04 2021

rule=28; 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]]], {k, 1, rows}] (* Binary Representation of Rows *)

(Python) print([(100*10**n + 89)//99 for n in range(50)]) # Karl V. Keller, Jr., Sep 04 2021

Cf. A266502, A283641, A283642.

Sequence in context: A283582 A283700 A284537 * A284424 A284545 A283645

Adjacent sequences: A266505 A266506 A266507 * A266509 A266510 A266511

nonn,easy

Robert Price, Dec 30 2015

approved