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

Author

Hans Havermann, May 26 2002

Keywords

• nonn
• tabf

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

Crossrefs

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

Programs

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

Mathematica

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

Formula

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

Extensions

Corrected by Hans Havermann, Jan 07 2012