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A266286 Number of OFF (white) cells in the n-th iteration of the "Rule 13" elementary cellular automaton starting with a single ON (black) cell. 1
0, 2, 3, 3, 6, 4, 9, 5, 12, 6, 15, 7, 18, 8, 21, 9, 24, 10, 27, 11, 30, 12, 33, 13, 36, 14, 39, 15, 42, 16, 45, 17, 48, 18, 51, 19, 54, 20, 57, 21, 60, 22, 63, 23, 66, 24, 69, 25, 72, 26, 75, 27, 78, 28, 81, 29, 84, 30, 87, 31, 90, 32, 93, 33, 96, 34, 99, 35 (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..999

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

FORMULA

Conjectures from Colin Barker, Dec 28 2015 and Apr 14 2019: (Start)

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

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

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

(End)

Conjecture: a(n) = (n^2)mod(2n-3) for n>6. - Andres Cicuttin, Aug 29 2019

Conjecture: E.g.f.: (1/4)*exp(-x)*(- 3 - 2*x + exp(2*x)*(3 + 4*x)). - Stefano Spezia, Aug 31 2019

MATHEMATICA

rule=13; 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. A266282.

Sequence in context: A049990 A173739 A062774 * A045892 A160791 A115973

Adjacent sequences:  A266283 A266284 A266285 * A266287 A266288 A266289

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 26 2015

STATUS

approved

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Last modified December 5 10:45 EST 2019. Contains 329751 sequences. (Running on oeis4.)