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A267049 Total number of OFF (white) cells after n iterations of the "Rule 91" elementary cellular automaton starting with a single ON (black) cell. 1
0, 1, 4, 7, 11, 14, 22, 25, 37, 40, 56, 59, 79, 82, 106, 109, 137, 140, 172, 175, 211, 214, 254, 257, 301, 304, 352, 355, 407, 410, 466, 469, 529, 532, 596, 599, 667, 670, 742, 745, 821, 824, 904, 907, 991, 994, 1082, 1085, 1177, 1180, 1276, 1279, 1379, 1382 (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..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 11 2016 and Apr 19 2019: (Start)

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

a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>6.

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

(End)

MATHEMATICA

rule=91; 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. A267015.

Sequence in context: A310733 A310734 A190774 * A310735 A003670 A084390

Adjacent sequences:  A267046 A267047 A267048 * A267050 A267051 A267052

KEYWORD

nonn

AUTHOR

Robert Price, Jan 09 2016

STATUS

approved

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Last modified May 10 01:36 EDT 2021. Contains 343747 sequences. (Running on oeis4.)