R, 3535 34 bytes
n=scan();(u=(n-n=scan(u=n%%2+1))^2-n%%2-1)/8+2-un+(15+u^2)/8 First output option.Same formula as many other answers (I'd like to point to the first answer providing the formula, I can't figure which it is).
Second and third output options below:
R, 43 bytes
function(m,n=1:m,u=n%%2+1)((n-u)^2-1)/8+2-u R, 51 bytes
while(T){cat(((T-(u=T%%2+1))^2-1)/8+2-u," ");T=T+1}