A266303 Number of ON (black) cells in the n-th iteration of the "Rule 15" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 1, 6, 1, 10, 1, 14, 1, 18, 1, 22, 1, 26, 1, 30, 1, 34, 1, 38, 1, 42, 1, 46, 1, 50, 1, 54, 1, 58, 1, 62, 1, 66, 1, 70, 1, 74, 1, 78, 1, 82, 1, 86, 1, 90, 1, 94, 1, 98, 1, 102, 1, 106, 1, 110, 1, 114, 1, 118, 1, 122, 1, 126, 1, 130, 1, 134, 1, 138, 1

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..999

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

Conjectures from Colin Barker, Dec 28 2015 and Apr 15 2019: (Start)

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

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

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

(End)

Mathematica

rule=15; 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[Total[catri[[k]]], {k, 1, rows}] (* Number of Black cells in stage n *)

Crossrefs

Cf. A266300.

Sequence in context: A274085 A302129 A191093 * A267354 A139625 A053785

Adjacent sequences: A266300 A266301 A266302 * A266304 A266305 A266306

Keyword

nonn,easy

Author

Robert Price, Dec 26 2015

Status

approved