|
|
A267212
|
|
Total number of ON (black) cells after n iterations of the "Rule 109" elementary cellular automaton starting with a single ON (black) cell.
|
|
1
|
|
|
1, 2, 7, 9, 16, 23, 33, 38, 51, 63, 76, 87, 105, 120, 139, 155, 176, 197, 221, 240, 267, 293, 320, 345, 377, 406, 439, 469, 504, 539, 577, 610, 651, 691, 732, 771, 817, 860, 907, 951, 1000, 1049, 1101, 1148, 1203, 1257, 1312, 1365, 1425, 1482, 1543, 1601
(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
|
|
|
FORMULA
|
Conjectures from Colin Barker, Jan 13 2016 and Apr 19 2019: (Start)
a(n) = a(n-1)+a(n-3)-a(n-5)-a(n-7)+a(n-8) for n>7.
G.f.: (1+x+5*x^2+x^3+5*x^4+x^5+3*x^6-3*x^7) / ((1-x)^3*(1+x)*(1+x^2)*(1+x+x^2)).
(End)
|
|
MATHEMATICA
|
rule=109; 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
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|