A266662 Number of ON (black) cells in the n-th iteration of the "Rule 47" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 2, 5, 2, 9, 2, 13, 2, 17, 2, 21, 2, 25, 2, 29, 2, 33, 2, 37, 2, 41, 2, 45, 2, 49, 2, 53, 2, 57, 2, 61, 2, 65, 2, 69, 2, 73, 2, 77, 2, 81, 2, 85, 2, 89, 2, 93, 2, 97, 2, 101, 2, 105, 2, 109, 2, 113, 2, 117, 2, 121, 2, 125, 2, 129, 2, 133, 2, 137, 2, 141

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..1000

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, Jan 03 2016 and Apr 18 2019: (Start)

a(n) = (-2*(-1)^n*n+2*n+3*(-1)^n+1)/2 for n>1.

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

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

(End)

a(n) = A266256(n), n>1. - R. J. Mathar, Jan 10 2016

Mathematica

rule=47; 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. A266659.

Sequence in context: A305808 A353858 A347466 * A289078 A051612 A083456

Adjacent sequences: A266659 A266660 A266661 * A266663 A266664 A266665

Keyword

nonn,easy

Author

Robert Price, Jan 02 2016

Status

approved