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A130047 Left half of Pascal's triangle (A034868) modulo 2. 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 (list; graph; refs; listen; history; text; internal format)
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: A192280 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

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)