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A267531 Total number of OFF (white) cells after n iterations of the "Rule 141" elementary cellular automaton starting with a single ON (black) cell. 1
0, 2, 5, 9, 13, 18, 23, 29, 35, 42, 49, 57, 65, 74, 83, 93, 103, 114, 125, 137, 149, 162, 175, 189, 203, 218, 233, 249, 265, 282, 299, 317, 335, 354, 373, 393, 413, 434, 455, 477, 499, 522, 545, 569, 593, 618, 643, 669, 695, 722, 749, 777, 805, 834, 863, 893 (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, Jan 17 2016: (Start)

a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n > 4.

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

(End)

Conjecture: a(n) = a(n-1) + A004526(n+5) for n > 1. - J. Stauduhar, Oct 21 2017

MATHEMATICA

rule=141; 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 *) nwc=Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}]; (* Number of White cells in stage n *) Table[Total[Take[nwc, k]], {k, 1, rows}] (* Number of White cells through stage n *)

CROSSREFS

Cf. A267525, A267530.

Sequence in context: A178805 A088907 A130235 * A219647 A129726 A122489

Adjacent sequences:  A267528 A267529 A267530 * A267532 A267533 A267534

KEYWORD

nonn

AUTHOR

Robert Price, Jan 16 2016

STATUS

approved

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Last modified October 17 04:09 EDT 2019. Contains 328106 sequences. (Running on oeis4.)