A267874 Total number of ON (black) cells after n iterations of the "Rule 235" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 6, 13, 22, 33, 46, 61, 78, 97, 118, 141, 166, 193, 222, 253, 286, 321, 358, 397, 438, 481, 526, 573, 622, 673, 726, 781, 838, 897, 958, 1021, 1086, 1153, 1222, 1293, 1366, 1441, 1518, 1597, 1678, 1761, 1846, 1933, 2022, 2113, 2206, 2301, 2398, 2497

Offset

0,2

Comments

With the exception of the first one or two entries the same as A123968 and A028872. - R. J. Mathar, Jan 24 2016

Links

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, 2002; p. 55.

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

From Colin Barker, Jan 22 2016 and Apr 20 2019: (Start)

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

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

(End)

Mathematica

rule=235; 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 *) nbc=Table[Total[catri[[k]]], {k, 1, rows}]; (* Number of Black cells in stage n *) Table[Total[Take[nbc, k]], {k, 1, rows}] (* Number of Black cells through stage n *)

Crossrefs

Cf. A267869.

Cf. A028872, A123968.

Sequence in context: A048072 A215246 A230537 * A194143 A194138 A194137

Adjacent sequences: A267871 A267872 A267873 * A267875 A267876 A267877

Keyword

nonn,easy

Author

Robert Price, Jan 21 2016

Status

approved