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A267353 Total number of ON (black) cells after n iterations of the "Rule 123" elementary cellular automaton starting with a single ON (black) cell. 1
1, 3, 6, 12, 15, 25, 28, 42, 45, 63, 66, 88, 91, 117, 120, 150, 153, 187, 190, 228, 231, 273, 276, 322, 325, 375, 378, 432, 435, 493, 496, 558, 561, 627, 630, 700, 703, 777, 780, 858, 861, 943, 946, 1032, 1035, 1125, 1128, 1222, 1225, 1323, 1326, 1428, 1431 (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 14 2016: (Start)

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

(End)

MATHEMATICA

rule=123; 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[Total[Take[nbc, k]], {k, 1, rows}] (* Number of Black cells through stage n *)

CROSSREFS

Cf. A267349.

Sequence in context: A115803 A290258 A277335 * A320607 A281063 A032602

Adjacent sequences:  A267350 A267351 A267352 * A267354 A267355 A267356

KEYWORD

nonn

AUTHOR

Robert Price, Jan 13 2016

STATUS

approved

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Last modified May 17 06:30 EDT 2021. Contains 343965 sequences. (Running on oeis4.)