A266792 Number of ON (black) cells in the n-th iteration of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 2, 5, 4, 7, 5, 11, 5, 15, 5, 19, 5, 23, 5, 27, 5, 31, 5, 35, 5, 39, 5, 43, 5, 47, 5, 51, 5, 55, 5, 59, 5, 63, 5, 67, 5, 71, 5, 75, 5, 79, 5, 83, 5, 87, 5, 91, 5, 95, 5, 99, 5, 103, 5, 107, 5, 111, 5, 115, 5, 119, 5, 123, 5, 127, 5, 131, 5, 135, 5, 139

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 04 2016 and Apr 18 2019: (Start)

a(n) = n+1-(-1)^n*(n-4) for n>4.

a(n) = 2*a(n-2)-a(n-4) for n>8.

G.f.: (1+2*x+x^3+x^4-x^5-x^6+2*x^7-x^8) / ((1-x)^2*(1+x)^2).

(End)

Mathematica

rule=61; 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. A266786.

Sequence in context: A284827 A241306 A336073 * A162200 A290289 A000019

Adjacent sequences: A266789 A266790 A266791 * A266793 A266794 A266795

Keyword

nonn,easy

Author

Robert Price, Jan 03 2016

Status

approved