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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
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 (list; graph; refs; listen; history; text; internal format)
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: A135534 A249904 A324875 * A077896 A046269 A153346

Adjacent sequences:  A266434 A266435 A266436 * A266438 A266439 A266440

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 29 2015

STATUS

approved

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Last modified July 11 01:42 EDT 2020. Contains 335600 sequences. (Running on oeis4.)