A266981 Number of ON (black) cells in the n-th iteration of the "Rule 79" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 2, 5, 3, 8, 4, 11, 5, 14, 6, 17, 7, 20, 8, 23, 9, 26, 10, 29, 11, 32, 12, 35, 13, 38, 14, 41, 15, 44, 16, 47, 17, 50, 18, 53, 19, 56, 20, 59, 21, 62, 22, 65, 23, 68, 24, 71, 25, 74, 26, 77, 27, 80, 28, 83, 29, 86, 30, 89, 31, 92, 32, 95, 33, 98, 34

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 08 2016 and Apr 19 2019: (Start)

a(n) = (3+(-1)^n-2*(-2+(-1)^n)*n)/4.

a(n) = 2*a(n-2)-a(n-4) for n>3.

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

(End)

Mathematica

rule=79; 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. A266978.

Sequence in context: A151729 A088652 A368207 * A045893 A071939 A338332

Adjacent sequences: A266978 A266979 A266980 * A266982 A266983 A266984

Keyword

nonn

Author

Robert Price, Jan 07 2016

Status

approved