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A266982
Triangle read by rows giving successive states of cellular automaton generated by "Rule 81" initiated with a single ON (black) cell.
3
1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1
OFFSET
0
COMMENTS
Row n has length 2n+1.
This sequence is also generated by rule 113.
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
Conjecture: a(0)=1; for n>0, a(n) = ( Sum_{i=1..n-2} floor((n-2)/i) ) mod 2. - Wesley Ivan Hurt, Mar 22 2016
EXAMPLE
The first ten rows:
1
0 0 1
1 1 0 0 0
0 0 1 1 1 1 1
1 1 0 0 0 0 0 0 0
0 0 1 1 1 1 1 1 1 1 1
1 1 0 0 0 0 0 0 0 0 0 0 0
0 0 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
MATHEMATICA
rule=81; 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 *) Flatten[catri] (* Triangle Representation of CA *)
CROSSREFS
Sequence in context: A188398 A288929 A285083 * A364746 A051341 A057211
KEYWORD
nonn,tabf,easy
AUTHOR
Robert Price, Jan 07 2016
STATUS
approved