A265281 Decimal representation of the n-th iteration of the "Rule 86" elementary cellular automaton starting with a single ON (black) cell.

1, 7, 19, 123, 275, 1915, 4627, 32379, 67347, 463739, 1276435, 8001147, 18245395, 124220283, 309475859, 2134808187, 4354074387, 30225757051, 82642024979, 530573137531, 1175676118803, 8199373878139, 19977819994643, 139441424012923, 286691477808915

Offset: 0

Author

Robert Price, Dec 06 2015

Keywords

• nonn
• easy

Comments

Iterates of A269161 starting from a(0) = 1. - Antti Karttunen, Feb 20 2016

Also, the decimal representation of the n-th generation of the "Rule 859583292" 5-neighbors elementary cellular automaton starting with a single ON (black) cell. - Philipp O. Tsvetkov, Jul 17 2019

References

• S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Links

• Robert Price, Table of n, a(n) for n = 0..999
• Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
• Index entries for sequences related to cellular automata
• Index to Elementary Cellular Automata

Crossrefs

Cf. A030101, A071032, A265280, A269161.

Cf. also A110240.

Programs

Mathematica

rule = 86; rows = 30; Table[FromDigits[Table[Take[CellularAutomaton[rule,{{1},0}, rows-1, {All,All}][[k]], {rows-k+1, rows+k-1}], {k,1,rows}][[k]],2], {k,1,rows}]

Formula

From Antti Karttunen, Feb 20 2016: (Start)

a(0) = 1, for n >= 1, a(n) = A269161(a(n-1)).

a(n) = A030101(A110240(n)). [The rule 86 is the mirror image of the rule 30.]

(End)