A266617 Total number of OFF (white) cells after n iterations of the "Rule 41" elementary cellular automaton starting with a single ON (black) cell.

0, 3, 6, 10, 18, 21, 32, 36, 52, 55, 74, 78, 102, 105, 132, 136, 168, 171, 206, 210, 250, 253, 296, 300, 348, 351, 402, 406, 462, 465, 524, 528, 592, 595, 662, 666, 738, 741, 816, 820, 900, 903, 986, 990, 1078, 1081, 1172, 1176, 1272, 1275, 1374, 1378, 1482

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 02 2016 and Apr 18 2019: (Start)

a(n) = a(n-1)+a(n-2)-a(n-3)+a(n-4)-a(n-5)-a(n-6)+a(n-7) for n>6.

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

(End)

Mathematica

rule=41; 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 *) nwc=Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}]; (* Number of White cells in stage n *) Table[Total[Take[nwc, k]], {k, 1, rows}] (* Number of White cells through stage n *)

Crossrefs

Cf. A266608.

Sequence in context: A092263 A259968 A242525 * A291608 A182152 A170803

Adjacent sequences: A266614 A266615 A266616 * A266618 A266619 A266620

Keyword

nonn

Author

Robert Price, Jan 01 2016

Status

approved