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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A303655 A011156 A213478 * A265536 A037849 A037885

Adjacent sequences:  A266446 A266447 A266448 * A266450 A266451 A266452

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 29 2015

STATUS

approved

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Last modified October 17 01:03 EDT 2019. Contains 328103 sequences. (Running on oeis4.)