A266220 Number of ON (black) cells in the n-th iteration of the "Rule 7" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 0, 7, 0, 11, 0, 15, 0, 19, 0, 23, 0, 27, 0, 31, 0, 35, 0, 39, 0, 43, 0, 47, 0, 51, 0, 55, 0, 59, 0, 63, 0, 67, 0, 71, 0, 75, 0, 79, 0, 83, 0, 87, 0, 91, 0, 95, 0, 99, 0, 103, 0, 107, 0, 111, 0, 115, 0, 119, 0, 123, 0, 127, 0, 131, 0, 135, 0, 139, 0

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..499

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 25 2015 and Apr 13 2019: (Start)

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

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

G.f.: (1+2*x-2*x^2+3*x^3+x^4-x^5) / ((1-x)^2*(1+x)^2).

(End)

Mathematica

rule=7; 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. A266216.

Sequence in context: A269430 A363891 A142709 * A022897 A192496 A156442

Adjacent sequences: A266217 A266218 A266219 * A266221 A266222 A266223

Keyword

nonn,easy

Author

Robert Price, Dec 24 2015

Status

approved