function [w]=gatecount(n)
%plots the discrepancy between the weight produced 
G=zeros(n,n); %G(r,k) is the number of r-qubit gates with k-1 controls in our decomposition
H=zeros(n,n); %H(r,k) is the number of r-qubit gates with k-1 controls in the Finnish paper
W=zeros(n,n); %weight matrix column k of G*W is column k of G times (k-1)
%s=zeros(2,n); %s(1,r) is the total number of controlled gates used in
               %decomposing U in G_r (our paper)
               %s(2,r) is the total number of controlled gates used in
               %decomposing U in G_r (Finnish paper) 
               %s(1,r)=s(2,r)=2^{r-1}(2^r-1) for all r 
               
w=zeros(2,n); %w(1,r)=T_1(r) and w(2,r)=T_2(r) as described in our conclusion
for r=1:n
    W(r,r)=r-1;
    G(r,1)=r;
    H(r,1)=2^(r-1);
    if r>1
    G(r,2)=r*(r-1)*(2^(r-2)+1);
        for k=2:r
            H(r,k)=H(r-1,k)+H(r-1,k-1)+ max([2^(r-2),2^(k-1)])+ 2^(2*r-k-1)-2^(r-2);
        end
    end
    if r>2
        G(r,3)=(1/3)*(4^r-4)-(2^r)*(r-1)+r*(r-1)*(r-2)/2;
    end
    if r>3
        for k=4:r
            G(r,k)=G(r-1,k)+G(r-1,k-1)+ nchoosek(r-1,k-1);
        end
    end
%s(1,r)=sum(G(r,:));
%s(2,r)=sum(H(r,:));
V=G*W;
X=H*W;
w(1,r)=sum(V(r,:));
w(2,r)=sum(X(r,:));
end

    x=1:n;
    plot(x,log10(w(2,:)-w(1,:)),'LineWidth', 2);
    ylabel('T2(n)-T1(n) in logarithm base 10');
    xlabel('n');
    title('Comparison of the total number of controls of our scheme and that of [7]')