A266439 Number of OFF (white) cells in the n-th iteration of the "Rule 23" elementary cellular automaton starting with a single ON (black) cell.

0, 0, 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..500

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, Dec 30 2015 and Apr 15 2019: (Start)

a(n) = ((-1)^n+1)*(2*n+1)/2 for n>0.

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

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

(End)

a(n) = A266222(n), n>1. - R. J. Mathar, Jan 10 2016

Mathematica

rule=23; 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. A266434.

Sequence in context: A344144 A372364 A266222 * A132706 A199184 A159692

Adjacent sequences: A266436 A266437 A266438 * A266440 A266441 A266442

Keyword

nonn,easy

Author

Robert Price, Dec 29 2015

Status

approved