Odd coefficients

by Philippe_57721

Let P[X,n] = (1 + X + X^2)^n
P[X,7] = X^14 + 7*X^13 + 28*X^12 + 77*X^11 + 161*X^10 + 266*X^9 + 357*X^8 + 393*X^7 + 357*X^6 + 266*X^5 + 161*X^4 + 77*X^3 + 28*X^2 + 7*X + 1
It contains 11 odd coefficients: 1,7,77,161,357,393,357,161,77,7,1

How many odd coefficients are there in P[X,6700417]?

[My timing: < 100 ms]