s(n)=2^(n+1)-1
a(1)=s(1)=2^2-1=3,
a(n+1)=s(n+1)-s(n)=2^(n+2)-2^(n+1)=2^(n+1)
a(1)=3,
a(n)=2^n,n=2,3,...
a(1)=3,
a(2k-1)=2^(2k-1)=2*2^(2k-2)=2*4^(k-1),k=2,3,...,n
a(1)+a(3)+...+a(2n-1)=3+2[1+4+...+4^(n-1)]=3+2[4^n-1]/(4-1)=3+(2/3)[4^n-1]