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A266722 Number of ON (black) cells in the n-th iteration of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell. 2
1, 2, 2, 6, 2, 10, 2, 14, 2, 18, 2, 22, 2, 26, 2, 30, 2, 34, 2, 38, 2, 42, 2, 46, 2, 50, 2, 54, 2, 58, 2, 62, 2, 66, 2, 70, 2, 74, 2, 78, 2, 82, 2, 86, 2, 90, 2, 94, 2, 98, 2, 102, 2, 106, 2, 110, 2, 114, 2, 118, 2, 122, 2, 126, 2, 130, 2, 134, 2, 138, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For n >= 3, also the number of maximum independent vertex sets in the n-prism graph. - Eric W. Weisstein, Mar 30 2017

For n >= 3, also the number of maximum independent edge sets in the n-web graph. - Eric W. Weisstein, Dec 31 2017

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

Eric Weisstein's World of Mathematics, Matching

Eric Weisstein's World of Mathematics, Maximum Independent Edge Set

Eric Weisstein's World of Mathematics, Maximum Independent Vertex Set

Eric Weisstein's World of Mathematics, Prism Graph

Eric Weisstein's World of Mathematics, Web Graph

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 05 2016 and Apr 17 2019: (Start)

a(n) = 1+(-1)^n+n-(-1)^n*n for n>0.

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

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

MATHEMATICA

rule=59; 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. A266716.

Sequence in context: A096869 A154009 A297792 * A232625 A099985 A298299

Adjacent sequences:  A266719 A266720 A266721 * A266723 A266724 A266725

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 03 2016

STATUS

approved

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Last modified June 25 04:06 EDT 2019. Contains 324345 sequences. (Running on oeis4.)