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A266440 Total number of OFF (white) cells after n iterations of the "Rule 23" elementary cellular automaton starting with a single ON (black) cell. 1
0, 0, 5, 5, 14, 14, 27, 27, 44, 44, 65, 65, 90, 90, 119, 119, 152, 152, 189, 189, 230, 230, 275, 275, 324, 324, 377, 377, 434, 434, 495, 495, 560, 560, 629, 629, 702, 702, 779, 779, 860, 860, 945, 945, 1034, 1034, 1127, 1127, 1224, 1224, 1325, 1325, 1430 (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..500

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, Dec 30 2015 and Apr 15 2019: (Start)

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

a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>4.

G.f.: x^2*(5-x^2) / ((1-x)^3*(1+x)^2).

(End)

MATHEMATICA

rule=23; 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. A266434.

Sequence in context: A062367 A286257 A168418 * A317617 A294750 A304300

Adjacent sequences:  A266437 A266438 A266439 * A266441 A266442 A266443

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 29 2015

STATUS

approved

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Last modified July 8 17:40 EDT 2020. Contains 335524 sequences. (Running on oeis4.)