0,1

Also triangle giving successive states of cellular automaton generated by "Rule 60" and "Rule 102". - Hans Havermann (pxp(AT)rogers.com), May 26 2002

Also triangle formed by reading triangle of Eulerian numbers (A08292) mod 2. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Oct 02 2003

Self-inverse when regarded as an infinite lower triangular matrix over GF(2).

Start with [1], repeatedly apply the map 0 -> [00/00], 1 -> [10/11] [Allouche and Berthe]

Also triangle formed by reading triangles A011117, A028338, A039757, A059438, A085881, A086646, A086872, A087903, A0104219 mod 2 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 18 2005

J. H. Conway writes (in Math Forum): at least the first 31 rows give odd-sided constructible polygons (sides 1, 3, 5, 15,17 ... see A001317). The 1's form a Sierpinski sieve. - M. Dauchez (mdzzdm(AT)yahoo.fr), Sep 19 2005

When regarded as an infinite lower triangular matrix, its inverse is a (-1,0,1)-matrix with zeros undisturbed and the nonzero entries in every column form the Prouhet-Thue-Morse sequence (1,-1,-1,1,-1,1,1,-1,...) A010060 (up to relabeling). - David Callan (callan(AT)stat.wisc.edu), Oct 27 2006

Triangle read by rows: antidiagonals of an array formed by successive iterates of running sums mod 2, beginning with (1, 1, 1,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 10 2008

R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), no. 8, 697-712.

Y. Moshe, The distribution of elements in automatic double sequences, Discr. Math., 297 (2005), 91-103.

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

T. D. Noe, Rows n=0..50 of triangle, flattened

J.-P. Allouche and V. Berthe, Triangle de Pascal, complexite et automates.

J. Baer, Explore patterns in Pascal's Triangle

A. Bogomolny, Dot Patterns and Sierpinski Gasket

S. Butkevich, Pascal Triangle Applet

B. Cherowitzo, Pascal's Triangle using Clock Arithmetic, Part I

B. Cherowitzo, Pascal's Triangle using Clock Arithmetic, Part II

A. Granville, Pascal's Triangle Interface

I. Kobayashi et al., Pascal's Triangle

Dr. Math, Regular polygon formulas>Regular polygon formulas

National Curve Bank, Sierpinski Triangles

F. Richman, Pascal's triangle modulo n

F. Richman, Pascal's triangle modulo n

Eric Weisstein's World of Mathematics, Sierpinski Sieve

Eric Weisstein's World of Mathematics, Rule 60

Eric Weisstein's World of Mathematics, Rule 102

Index entries for sequences related to cellular automata

Index entries for triangles and arrays related to Pascal's triangle

Index entries for sequences generated by sieves

Sum_{k>=0} T(n, k) = A001316(n) = 2^A000120(n).

Triangle begins:

.1,

.1,1,

.1,0,1,

.1,1,1,1,

.1,0,0,0,1,

.1,1,0,0,1,1,

.1,0,1,0,1,0,1,

.1,1,1,1,1,1,1,1,

.1,0,0,0,0,0,0,0,1,

.1,1,0,0,0,0,0,0,1,1,

.1,0,1,0,0,0,0,0,1,0,1,

.1,1,1,1,0,0,0,0,1,1,1,1,

.1,0,0,0,1,0,0,0,1,0,0,0,1,

....

Mod[ Flatten[ NestList[ Prepend[ #, 0] + Append[ #, 0] &, {1}, 13]], 2] (from Robert G. Wilson v May 26 2004)

Contribution from Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Oct 10 2009: (Start)

(PARI) \\ Recurrence for Pascal's triangle mod p, here p = 2.

p = 2; s=13; T=matrix(s, s); T[1, 1]=1;

for(n=2, s, T[n, 1]=1; for(k=2, n, T[n, k] = (T[n-1, k-1] + T[n-1, k])%p ));

for(n=1, s, for(k=1, n, print1(T[n, k], ", "))) (End)

Cf. A007318, A054431, A001317, A008292, A083093, A034931, A034930, A008975, A034932.

Sequence in context: A144093 A143200 A166282 this_sequence A054431 A164381 A106470

Adjacent sequences: A047996 A047997 A047998 this_sequence A048000 A048001 A048002

nonn,tabl,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).

Additional links from Lekraj Beedassy (blekraj(AT)yahoo.com), Jan 22 2004