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A266665 Total number of OFF (white) cells after n iterations of the "Rule 47" elementary cellular automaton starting with a single ON (black) cell. 1
0, 1, 4, 6, 13, 15, 26, 28, 43, 45, 64, 66, 89, 91, 118, 120, 151, 153, 188, 190, 229, 231, 274, 276, 323, 325, 376, 378, 433, 435, 494, 496, 559, 561, 628, 630, 701, 703, 778, 780, 859, 861, 944, 946, 1033, 1035, 1126, 1128, 1223, 1225, 1324, 1326, 1429 (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
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
FORMULA
Conjectures from Colin Barker, Jan 03 2016 and Apr 18 2019: (Start)
a(n) = (n^2+2*n+(-1)^n*(n-1)-1)/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.: x*(1+3*x+x^3-x^4) / ((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 *) 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. A266659.
Sequence in context: A137821 A010061 A280557 * A249715 A249440 A063186
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 02 2016
STATUS
approved

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Last modified June 15 22:50 EDT 2024. Contains 373412 sequences. (Running on oeis4.)