OFFSET
0
COMMENTS
Row n has length 2n+1.
This sequence is also generated by Rule 238.
LINKS
Robert Price, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
Conjecture: a(n) = (1 + (-1)^floor(2*sqrt(n)))/2. - Velin Yanev, Nov 30 2016
a(n) = A351319(n) for n != 2. - Chai Wah Wu, Jul 29 2022
EXAMPLE
The first ten rows:
1
1 1 0
1 1 1 0 0
1 1 1 1 0 0 0
1 1 1 1 1 0 0 0 0
1 1 1 1 1 1 0 0 0 0 0
1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0
MATHEMATICA
rule=206; 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 *)
PROG
(Python)
from math import isqrt
def A267708(n): return int((k:=isqrt(n))**2+k-n+1>0) # Chai Wah Wu, Jul 28 2022
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
Robert Price, Jan 19 2016
STATUS
approved