A071032 Triangle read by rows giving successive states of cellular automaton generated by "Rule 86".

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

Offset

0,1

Comments

Row n has length 2n+1.

References

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.

Links

Reinhard Zumkeller, Rows n = 0..120 of triangle, flattened

Eric Weisstein's World of Mathematics, Rule 30

S. Wolfram, A New Kind of Science

Index to Elementary Cellular Automata

Index entries for sequences related to cellular automata

Formula

T(n,k) = A070950(n,2*n+1-k), 0 <= k <= 2*n+1. - Reinhard Zumkeller, Jun 08 2013

Mathematica

A071032list[rowmax_]:=MapIndexed[ArrayPad[#1, #2-rowmax-1]&, CellularAutomaton[86, {{1}, 0}, rowmax]]; A071032list[10] (* Generates 11 rows *) (* Paolo Xausa, Jun 01 2023 *)

Prog

(Haskell)
a071032 n k = a071032_tabf !! n !! k
a071032_row n = a071032_tabf !! n
a071032_tabf = map reverse a070950_tabf
-- Reinhard Zumkeller, Jun 08 2013

Crossrefs

Cf. A005408 (row lengths), A070952 (row sums), A051023 (central terms), A070950 (mirror image, rule 30), A226464 (complemented, rule 149).

Sequence in context: A104037 A014044 A014079 * A071034 A089497 A355937

Adjacent sequences: A071029 A071030 A071031 * A071033 A071034 A071035

Keyword

nonn,tabf

Author

Hans Havermann, May 26 2002

Extensions

Corrected by Hans Havermann, Jan 07 2012

Status

approved