A266723 Total number of ON (black) cells after n iterations of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 5, 11, 13, 23, 25, 39, 41, 59, 61, 83, 85, 111, 113, 143, 145, 179, 181, 219, 221, 263, 265, 311, 313, 363, 365, 419, 421, 479, 481, 543, 545, 611, 613, 683, 685, 759, 761, 839, 841, 923, 925, 1011, 1013, 1103, 1105, 1199, 1201, 1299, 1301, 1403, 1405

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 05 2016 and Apr 18 2019: (Start)

a(n) = (3+(-1)^n-2*(-3+(-1)^n)*n+2*n^2)/4.

a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>4.

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

(End)

Mathematica

rule=59; 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. A266716.

Sequence in context: A295243 A179017 A078971 * A129096 A079448 A045407

Adjacent sequences: A266720 A266721 A266722 * A266724 A266725 A266726

Keyword

nonn

Author

Robert Price, Jan 03 2016

Status

approved