A267048 Number of OFF (white) cells in the n-th iteration of the "Rule 91" elementary cellular automaton starting with a single ON (black) cell.

0, 1, 3, 3, 4, 3, 8, 3, 12, 3, 16, 3, 20, 3, 24, 3, 28, 3, 32, 3, 36, 3, 40, 3, 44, 3, 48, 3, 52, 3, 56, 3, 60, 3, 64, 3, 68, 3, 72, 3, 76, 3, 80, 3, 84, 3, 88, 3, 92, 3, 96, 3, 100, 3, 104, 3, 108, 3, 112, 3, 116, 3, 120, 3, 124, 3, 128, 3, 132, 3, 136, 3

Offset

0,3

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 11 2016 and Apr 19 2019: (Start)

a(n) = (2*(-1)^n*n+2*n-7*(-1)^n-1)/2 for n>2.

a(n) = 2*a(n-2)-a(n-4) for n>6.

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

(End)

Mathematica

rule=91; 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[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}] (* Number of White cells in stage n *)

Crossrefs

Cf. A267015.

Sequence in context: A163375 A027011 A339400 * A350502 A326401 A326415

Adjacent sequences: A267045 A267046 A267047 * A267049 A267050 A267051

Keyword

nonn

Author

Robert Price, Jan 09 2016

Status

approved