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
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
KEYWORD
nonn,tabf
AUTHOR
Hans Havermann, May 26 2002
EXTENSIONS
Corrected by Hans Havermann, Jan 08 2012
STATUS
approved