A266593 Number of ON (black) cells in the n-th iteration of the "Rule 37" elementary cellular automaton starting with a single ON (black) cell.

1, 1, 3, 2, 3, 6, 3, 10, 3, 14, 3, 18, 3, 22, 3, 26, 3, 30, 3, 34, 3, 38, 3, 42, 3, 46, 3, 50, 3, 54, 3, 58, 3, 62, 3, 66, 3, 70, 3, 74, 3, 78, 3, 82, 3, 86, 3, 90, 3, 94, 3, 98, 3, 102, 3, 106, 3, 110, 3, 114, 3, 118, 3, 122, 3, 126, 3, 130, 3, 134, 3, 138

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 02 2016 and Apr 18 2019: (Start)

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

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

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

(End)

Mathematica

rule=37; 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. A266588.

Sequence in context: A240162 A113128 A220075 * A130459 A323621 A144216

Adjacent sequences: A266590 A266591 A266592 * A266594 A266595 A266596

Keyword

nonn,easy

Author

Robert Price, Jan 01 2016

Status

approved