A006978 Successive states of the Rule 110 cellular automaton defined by 000, 001, 010, 011, ..., 111 -> 0,1,1,1,0,1,1,0 when started with a single ON cell.

1, 3, 7, 13, 31, 49, 115, 215, 509, 775, 1805, 3359, 7985, 12659, 29655, 54909, 130759, 197581, 460383, 855793, 2038675, 3227319, 7562237, 14149127, 33304077, 50625055, 118279729, 220060275, 523730647, 830325757, 1942439431, 3595423245, 8571017759, 12951092785

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• Marc LeBrun, personal communication.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Paolo Xausa, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Rule 110
• Index entries for sequences related to cellular automata

Crossrefs

Cf. A070887, A117999.

Programs

Mathematica

Map[FromDigits[#, 2] &, CellularAutomaton[110, {{1}, 0}, 30]] (* Ben Branman, Dec 28 2010 *)

Formula

a(n) = A117999(n-1)/2^(n-1). - Pontus von Brömssen, Oct 18 2022

Extensions

More terms from Eric W. Weisstein, Apr 11 2006

Definition clarified by N. J. A. Sloane, Oct 18 2022