A266222 Number of OFF (white) cells in the n-th iteration of the "Rule 7" elementary cellular automaton starting with a single ON (black) cell.

0, 1, 5, 0, 9, 0, 13, 0, 17, 0, 21, 0, 25, 0, 29, 0, 33, 0, 37, 0, 41, 0, 45, 0, 49, 0, 53, 0, 57, 0, 61, 0, 65, 0, 69, 0, 73, 0, 77, 0, 81, 0, 85, 0, 89, 0, 93, 0, 97, 0, 101, 0, 105, 0, 109, 0, 113, 0, 117, 0, 121, 0, 125, 0, 129, 0, 133, 0, 137, 0, 141, 0

Offset

0,3

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 26 2015 and Apr 13 2019: (Start)

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

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

G.f.: x*(1+5*x-2*x^2-x^3+x^4) / ((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 *) nbc=Table[Total[catri[[k]]], {k, 1, rows}]; (* Number of Black cells in stage n *) Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}] (* Number of White cells in stage n *)

Crossrefs

Cf. A266216.

Sequence in context: A141431 A166011 A344144 * A266439 A132706 A199184

Adjacent sequences: A266219 A266220 A266221 * A266223 A266224 A266225

Keyword

nonn,easy

Author

Robert Price, Dec 24 2015

Status

approved