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A266724 Number of OFF (white) cells in the n-th iteration of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell. 1
0, 1, 3, 1, 7, 1, 11, 1, 15, 1, 19, 1, 23, 1, 27, 1, 31, 1, 35, 1, 39, 1, 43, 1, 47, 1, 51, 1, 55, 1, 59, 1, 63, 1, 67, 1, 71, 1, 75, 1, 79, 1, 83, 1, 87, 1, 91, 1, 95, 1, 99, 1, 103, 1, 107, 1, 111, 1, 115, 1, 119, 1, 123, 1, 127, 1, 131, 1, 135, 1, 139, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

FORMULA

From Colin Barker, Jan 05 2016: (Start)

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

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

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

PROG

(PARI) concat(0, vector(80, n, n--; (-1)^(n+1)*n+n+1)) \\ Colin Barker, Jan 05 2016

CROSSREFS

Cf. A266716.

Sequence in context: A086665 A273013 A050521 * A247146 A225561 A098093

Adjacent sequences:  A266721 A266722 A266723 * A266725 A266726 A266727

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 03 2016

STATUS

approved

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Last modified March 26 04:32 EDT 2019. Contains 321481 sequences. (Running on oeis4.)