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

0,1

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).

Links

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

Formula

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

Example

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,
...

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 *)

Crossrefs

Cf. A007318, A034868, A048896, A133179.

Sequence in context: A354355 A266974 A075437 * A293233 A302050 A008683

Adjacent sequences: A130044 A130045 A130046 * A130048 A130049 A130050

Keyword

nonn,tabf

Author

Philippe Deléham, Oct 10 2007

Extensions

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

Status

approved