A130047 Left half of Pascal's triangle (A034868) modulo 2.

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

Offset: 0

Author

Philippe Deléham, Oct 10 2007

Keywords

• nonn
• tabf

Comments

Row sums yield: 1, 1, 1, 2, 1, 2, 2, 4, 1, 2, 2, 4, 2, 4, 4, 8, 1, 2, 2, 4, 2, 4, 4, 8, ...(see A048896).

Examples

			Triangle begins:
1,
1,
1, 0,
1, 1,
1, 0, 0,
1, 1, 0,
1, 0, 1, 0,
1, 1, 1, 1,
1, 0, 0, 0, 0,
1, 1, 0, 0, 0,
1, 0, 1, 0, 0, 0,
1, 1, 1, 1, 0, 0,
1, 0, 0, 0, 1, 0, 0,
1, 1, 0, 0, 1, 1, 0,
1, 0, 1, 0, 1, 0, 1, 0,
1, 1, 1, 1, 1, 1, 1, 1,
1, 0, 0, 0, 0, 0, 0, 0, 0,
...
Triangle (right aligned) begins:
                                  1,
                                1,
                              1,  0,
                            1,  1,
                          1,  0,  0,
                        1,  1,  0,
                      1,  0,  1,  0,
                    1,  1,  1,  1,
                  1,  0,  0,  0,  0,
                1,  1,  0,  0,  0,
              1,  0,  1,  0,  0,  0,
            1,  1,  1,  1,  0,  0,
          1,  0,  0,  0,  1,  0,  0,
        1,  1,  0,  0,  1,  1,  0,
      1,  0,  1,  0,  1,  0,  1,  0,
    1,  1,  1,  1,  1,  1,  1,  1,
  1,  0,  0,  0,  0,  0,  0,  0,  0,
1,  1,  0,  0,  0,  0,  0,  0,  0,
...
		

Links

• G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened

Crossrefs

Cf. A007318, A034868, A048896, A133179.

Programs

Maple

# From N. J. A. Sloane, Mar 22 2015:
for n from 0 to 20 do
lprint(seq(binomial(n,k) mod 2, k=0..floor(n/2))); od:
# For row sums:
f:=n->add(binomial(n,k) mod 2, k=0..floor(n/2));
[seq(f(n),n=0..60)];

Mathematica

Table[Mod[Binomial[n, k], 2], {n, 0, 10}, {k, 0, Floor[n/2]}] (* G. C. Greubel, Aug 12 2017 *)

Formula

T(n,k) = mod(binomial(n, k), 2), 0 <= k <= floor(n/2). - G. C. Greubel, Aug 12 2017

Extensions

Corrected by N. J. A. Sloane, Mar 22 2015 at the suggestion of Kevin Ryde