OFFSET
1,1
COMMENTS
New state of cell is 1 in every case except when the previous states of the cell and its two neighbors were all the same, or when the left neighbor was 1 and the cell and its right neighbor were both 0.
A cellular automaton using Rule 110 with arbitrary inputs is a universal Turing machine.
Row n has length n.
T(n,k) = A075437(n-1,k-1), k=1..n. - Reinhard Zumkeller, Jun 26 2013
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 31ff..
LINKS
Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened
Eric Weisstein's World of Mathematics, Rule 110
Wikipedia, Rule 110
EXAMPLE
1;
1,1;
1,1,1;
1,1,0,1;
1,1,1,1,1; ...
MAPLE
A070887 := proc(n, k)
option remember;
local lef, mid, rig ;
if k < 1 or k > n then
0;
elif n = 1 then
1;
else
lef := procname(n-1, k-2) ;
mid := procname(n-1, k-1) ;
rig := procname(n-1, k) ;
if lef = mid and mid = rig then
0 ;
elif lef = 1 and mid =0 and rig =0 then
0;
else
1 ;
end if;
end if;
end proc:
for n from 1 to 12 do
for k from 1 to n do
printf("%d ", A070887(n, k)) ;
end do:
printf("\n")
end do: # R. J. Mathar, Feb 18 2015
MATHEMATICA
rows = 14; ca = CellularAutomaton[110, {{1}, 0}, rows-1]; Flatten[ Table[ca[[k, rows-k+1 ;; -1]], {k, 1, rows}]] (* Jean-François Alcover, May 24 2012 *)
PROG
(Haskell)
a070887 n k = a070887_tabl !! (n-1) !! (k-1)
a070887_row n = a070887_tabl !! (n-1)
a070887_tabl = zipWith take [1..] a075437_tabf
-- Reinhard Zumkeller, Jun 26 2013
CROSSREFS
KEYWORD
AUTHOR
N. J. A. Sloane, May 19 2002
EXTENSIONS
More terms from Hans Havermann, May 26 2002
STATUS
approved