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 A070887 Triangle read by rows giving successive states of one-dimensional cellular automaton generated by "Rule 110". 8
 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 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 Cf. A070950, A070886. Cf. A047999. A071049 gives number of ON cells at n-th generation. Sequence in context: A334460 A071023 A166280 * A209635 A110242 A273592 Adjacent sequences:  A070884 A070885 A070886 * A070888 A070889 A070890 KEYWORD nonn,tabl,nice,easy AUTHOR N. J. A. Sloane, May 19 2002 EXTENSIONS More terms from Hans Havermann, May 26 2002 STATUS approved

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Last modified September 30 13:46 EDT 2020. Contains 337439 sequences. (Running on oeis4.)