

A267884


Total number of OFF (white) cells after n iterations of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell.


1



0, 3, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6
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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
Index entries for linear recurrences with constant coefficients, signature (1).


FORMULA

From Colin Barker, Jan 24 2016: (Start)
a(n) = 6 for n>2.
a(n) = a(n1) for n>3.
G.f.: x*(3+2*x+x^2) / (1x).
(End)


MATHEMATICA

rule=233; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rowsk+1, rows+k1}], {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 *)


PROG

(PARI) concat(0, Vec(x*(3+2*x+x^2)/(1x) + O(x^100))) \\ Colin Barker, Jan 24 2016


CROSSREFS

Cf. A267868.
Sequence in context: A161435 A224831 A281591 * A077859 A123572 A244953
Adjacent sequences: A267881 A267882 A267883 * A267885 A267886 A267887


KEYWORD

nonn,easy


AUTHOR

Robert Price, Jan 21 2016


STATUS

approved



