The sum of the coefficients of even power of x in the expansion of 1+x+x2+x35 is

1+x+x2+x35=a0+a1x+a2x2+a3x3+⋯+a15x15Putting x = 1 and x = -1 alternatively, we havea0+a1+a2+a3+⋯+a15=45         (1)a0−a1+a2−a3+⋯−a15=0           (2)Adding (1) and (2), we have2a0+a2+a4+⋯+a14=45or  a0+a2+a4+⋯+a14=29=512