Faster way to calculate the amount of odd coefficients of $(x+1)^{1000}$

Question

Is there a faster way to calculate the amount of odd coefficients of $(x+1)^{1000}$ besides going over all the options with the combinations formula?

I also tried to look at the amount of odd coefficients by going over the first $10$ series of Pascal's triangle to get a sequence. I didn't find it.

Related: https://math.stackexchange.com/questions/11002/cn-p-even-or-odd — Patrick Stevens, Mar 09 '16 at 14:18

score 0 · Answer 1 · answered Mar 09 '16 at 16:11

0

Use recurrence relations for n!/(n-r)!

There are quite a few, work from smaller n to larger n.

answered Mar 09 '16 at 16:11

Arif Burhan

1 Answers1