A070886 Triangle read by rows giving successive states of cellular automaton generated by "Rule 90".

1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0

Offset: 0

Author

N. J. A. Sloane, May 19 2002

Keywords

• nonn
• tabf
• nice
• easy

Comments

If either neighbor is 1 then new state is 1, otherwise new state is 0.

Row n has length 2n+1.

Rules #18, #26, #82, #90, #146, #154, #210, #218 all give rise to this sequence. - Hans Havermann

Examples

			1; 1,0,1; 1,0,0,0,1; 1,0,1,0,1,0,1; ...
		

References

• S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 25.

Links

• Robert Price, Table of n, a(n) for n = 0..9999
• Eric Weisstein's World of Mathematics, Rule 90
• S. Wolfram, A New Kind of Science
• Index to Elementary Cellular Automata
• Index entries for sequences related to cellular automata

Crossrefs

Cf. A070950, A070887. Alternate rows of A047999. Interpreted as binary numbers: A038183. Interpreted as Zeckendorf-expansions: A048757. Drawn as binary trees: A080263.

Programs

Mathematica

rows = 10; ca = CellularAutomaton[90, {{1}, 0}, rows-1]; Flatten[ Table[ca[[k, rows-k+1 ;; rows+k-1]], {k, 1, rows}]] (* Jean-François Alcover, May 24 2012 *)

Extensions

More terms from Hans Havermann, May 26 2002