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, 2004433876841339

Offset

0,2

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

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)

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}]
NestList[BitXor[4*#, BitOr[#, 2*#]] &, 1, 25] (* Paolo Xausa, Feb 05 2026 *)

Prog

(Scheme) ;; With memoization-macro definec.
(definec (A265281 n) (if (zero? n) 1 (A269161 (A265281 (- n 1)))))
;; Antti Karttunen, Feb 20 2016

Crossrefs

Cf. A030101, A071032, A265280, A269161.

Cf. also A110240.

Sequence in context: A180025 A070976 A249608 * A267276 A328713 A376907

Adjacent sequences: A265278 A265279 A265280 * A265282 A265283 A265284

Keyword

nonn,easy

Author

Robert Price, Dec 06 2015

Status

approved