A266663 Total number of ON (black) cells after n iterations of the "Rule 47" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 5, 10, 12, 21, 23, 36, 38, 55, 57, 78, 80, 105, 107, 136, 138, 171, 173, 210, 212, 253, 255, 300, 302, 351, 353, 406, 408, 465, 467, 528, 530, 595, 597, 666, 668, 741, 743, 820, 822, 903, 905, 990, 992, 1081, 1083, 1176, 1178, 1275, 1277, 1378, 1380

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) = (n^2-(-1)^n*n+2*n+(-1)^n+3)/2 for n>0.

a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>5.

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

(End)

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 *) nbc=Table[Total[catri[[k]]], {k, 1, rows}]; (* Number of Black cells in stage n *) Table[Total[Take[nbc, k]], {k, 1, rows}] (* Number of Black cells through stage n *)

Crossrefs

Cf. A266659.

Sequence in context: A285679 A093661 A080561 * A007557 A034746 A345176

Adjacent sequences: A266660 A266661 A266662 * A266664 A266665 A266666

Keyword

nonn,easy

Author

Robert Price, Jan 02 2016

Status

approved