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A266663 Total number of ON (black) cells after n iterations of the "Rule 47" elementary cellular automaton starting with a single ON (black) cell. 1
1, 3, 5, 10, 12, 21, 23, 36, 38, 55, 57, 78, 80, 105, 107, 136, 138, 171, 173, 210, 212, 253, 255, 300, 302, 351, 353, 406, 408, 465, 467, 528, 530, 595, 597, 666, 668, 741, 743, 820, 822, 903, 905, 990, 992, 1081, 1083, 1176, 1178, 1275, 1277, 1378, 1380 (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

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

FORMULA

From Colin Barker, Jan 03 2016: (Start)

a(n) = (n^2-(-1)^n*n+2*n+(-1)^n+3)/2 for n>0.

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

G.f.: (1+2*x+x^3-x^4+x^5) / ((1-x)^3*(1+x)^2).

(End)

MATHEMATICA

rule=47; 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 *)

PROG

(PARI) Vec((1+2*x+x^3-x^4+x^5)/((1-x)^3*(1+x)^2) + O(x^100)) \\ Colin Barker, Jan 03 2016

CROSSREFS

Cf. A266659.

Sequence in context: A285679 A093661 A080561 * A007557 A034746 A275219

Adjacent sequences:  A266660 A266661 A266662 * A266664 A266665 A266666

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 02 2016

STATUS

approved

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Last modified March 26 16:33 EDT 2019. Contains 321510 sequences. (Running on oeis4.)