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A266438 Total number of ON (black) cells after n iterations of the "Rule 23" elementary cellular automaton starting with a single ON (black) cell. 1
1, 4, 4, 11, 11, 22, 22, 37, 37, 56, 56, 79, 79, 106, 106, 137, 137, 172, 172, 211, 211, 254, 254, 301, 301, 352, 352, 407, 407, 466, 466, 529, 529, 596, 596, 667, 667, 742, 742, 821, 821, 904, 904, 991, 991, 1082, 1082, 1177, 1177, 1276, 1276, 1379, 1379 (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..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

Conjectured g.f.: (-(1 + x)^(-2) + (-3 + 3*x - 2*x^2)/(-1 + x)^3)/2. - Michael De Vlieger, Dec 29 2015

Conjectures from Colin Barker, Dec 30 2015 and Apr 15 2019: (Start)

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

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

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

CROSSREFS

Cf. A266434.

Sequence in context: A107856 A212102 A168373 * A128499 A325859 A265206

Adjacent sequences:  A266435 A266436 A266437 * A266439 A266440 A266441

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 29 2015

STATUS

approved

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Last modified May 29 20:42 EDT 2020. Contains 334710 sequences. (Running on oeis4.)