A266449 Number of OFF (white) cells in the n-th iteration of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell.

0, 2, 3, 4, 5, 5, 9, 5, 13, 5, 17, 5, 21, 5, 25, 5, 29, 5, 33, 5, 37, 5, 41, 5, 45, 5, 49, 5, 53, 5, 57, 5, 61, 5, 65, 5, 69, 5, 73, 5, 77, 5, 81, 5, 85, 5, 89, 5, 93, 5, 97, 5, 101, 5, 105, 5, 109, 5, 113, 5, 117, 5, 121, 5, 125, 5, 129, 5, 133, 5, 137, 5

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, Dec 30 2015 and Apr 16 2019: (Start)

a(n) = (-1)^n*(n-4)+n+1 for n>3.

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

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

(End)

Mathematica

rule=25; 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. A266441.

Sequence in context: A011156 A213478 A332782 * A265536 A037849 A037885

Adjacent sequences: A266446 A266447 A266448 * A266450 A266451 A266452

Keyword

nonn,easy

Author

Robert Price, Dec 29 2015

Status

approved