A267046 Number of ON (black) cells in the n-th iteration of the "Rule 91" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 2, 4, 5, 8, 5, 12, 5, 16, 5, 20, 5, 24, 5, 28, 5, 32, 5, 36, 5, 40, 5, 44, 5, 48, 5, 52, 5, 56, 5, 60, 5, 64, 5, 68, 5, 72, 5, 76, 5, 80, 5, 84, 5, 88, 5, 92, 5, 96, 5, 100, 5, 104, 5, 108, 5, 112, 5, 116, 5, 120, 5, 124, 5, 128, 5, 132, 5, 136, 5, 140

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 10 2016 and Apr 19 2019: (Start)

a(n) = 3/2+(7*(-1)^n)/2+n-(-1)^n*n for n>2.

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

G.f.: (1+2*x+2*x^4+2*x^5-3*x^6) / ((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 *) Table[Total[catri[[k]]], {k, 1, rows}] (* Number of Black cells in stage n *)

Crossrefs

Cf. A267015.

Sequence in context: A292382 A296561 A300121 * A308902 A166515 A339560

Adjacent sequences: A267043 A267044 A267045 * A267047 A267048 A267049

Keyword

nonn,easy

Author

Robert Price, Jan 09 2016

Status

approved