A071036 Triangle read by rows giving successive states of cellular automaton generated by "Rule 150" when started with a single ON cell.

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

Offset

0,1

Comments

Row n has length 2n+1.

Also the coefficients of (x^2 + x + 1)^n mod 2. - Alan DenAdel, Mar 19 2014

The number of 0's in row n is A071052(n), and the number of 1's in row n is A071053(n). - Michael Somos, Jun 24 2018

References

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

Links

Robert Price, Table of n, a(n) for n = 0..9999

Rémy Sigrist, Representation of the first 2^10 rows of the table

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index to Elementary Cellular Automata

Index entries for sequences related to cellular automata

Formula

a(n) = A027907(n) modulo 2. - Michel Marcus, Mar 20 2014

Example

Triangle begins:
1;
1, 1, 1;
1, 0, 1, 0, 1;
1, 1, 0, 1, 0, 1, 1;
1, 0, 0, 0, 1, 0, 0, 0, 1;
1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1;
... - Michel Marcus, Mar 20 2014

Mathematica

T[ n_, k_] := T[n, k] = Which[k < 0 || k > 2 n, 0, n == k == 0, 1, True, Mod[ T[n - 1, k - 2] + T[n - 1, k - 1] + T[n - 1, k], 2]]; (* Michael Somos, Jun 24 2018 *)

Prog

(PARI) rown(n) = Vec(lift((x^2 + x + 1)^n * Mod(1, 2))); \\ Michel Marcus, Mar 20 2014

Crossrefs

Cf. A027907, A071052, A071053.

This sequence, A038184 and A118110 are equivalent descriptions of the Rule 150 automaton.

Sequence in context: A344864 A140653 A342892 * A071038 A131522 A221641

Adjacent sequences: A071033 A071034 A071035 * A071037 A071038 A071039

Keyword

nonn,tabf

Author

Hans Havermann, May 26 2002

Extensions

Corrected by Hans Havermann, Jan 08 2012

Status

approved