A266794 Number of OFF (white) cells in the n-th iteration of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.

0, 1, 3, 2, 5, 4, 8, 4, 12, 4, 16, 4, 20, 4, 24, 4, 28, 4, 32, 4, 36, 4, 40, 4, 44, 4, 48, 4, 52, 4, 56, 4, 60, 4, 64, 4, 68, 4, 72, 4, 76, 4, 80, 4, 84, 4, 88, 4, 92, 4, 96, 4, 100, 4, 104, 4, 108, 4, 112, 4, 116, 4, 120, 4, 124, 4, 128, 4, 132, 4, 136, 4

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 04 2016 and Apr 17 2019: (Start)

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

a(n) = 2*a(n-2)-a(n-4) for n>7.

G.f.: x*(1+3*x-x^3+x^4+x^5-2*x^6+x^7) / ((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 *) 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. A266786.

Cf. A266795 (partial sums).

Sequence in context: A164380 A143527 A284153 * A340286 A194078 A169752

Adjacent sequences: A266791 A266792 A266793 * A266795 A266796 A266797

Keyword

nonn,easy

Author

Robert Price, Jan 03 2016

Status

approved