A266437 Number of ON (black) cells in the n-th iteration of the "Rule 23" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 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..500

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

Empirical g.f.: (1 + 3*x - 2*x^2 + x^3 + x^4)/(-1 + x^2)^2. - Michael De Vlieger, Dec 29 2015

Conjectures from Colin Barker, Dec 30 2015 and Apr 15 2019: (Start)

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

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

(End)

a(n) = A266220(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 *) Table[Total[catri[[k]]], {k, 1, rows}] (* Number of Black cells in stage n *)

Crossrefs

Cf. A266434.

Sequence in context: A337767 A249904 A324875 * A077896 A359061 A238942

Adjacent sequences: A266434 A266435 A266436 * A266438 A266439 A266440

Keyword

nonn,easy

Author

Robert Price, Dec 29 2015

Status

approved