How to sum up a matrix with upper diagonal direction without for-loop condition

How can I make the following 2-D matrix into 1D matrix by summing up the 2-D matrix with upper diagonal direction with no use of for-loop condition?

A= [ 1 2 3 4 5 6 7 8 9; 2 3 4 5 6 7 8 9 10; 3 4 5 6 7 8 9 10 11;]

B = [1 4 9 12 15 18 21 24 27 20 11];

More detail, B = [1 (2+2) (3+3+3) (4+4+4) (5+5+5) (6+6+6) (7+7+7) (8+8+8) (9+9+9) (10+10) (11)];

Answer 1

[Azzi Abdelmalek]

A= [ 1 2 3 4 5 6 7 8 9; 2 3 4 5 6 7 8 9 10; 3 4 5 6 7 8 9 10 11];
[n,m]=size(A);
A(:,end+1:end+n-1)=0;
B=sum(cell2mat(arrayfun(@(x) circshift(A(x,:),[0 x-1]),(1:n)','un',0')))

Answer 2

[Azzi Abdelmalek]

This one should be faster

A= [ 1 2 3 4 5 6 7 8 9; 2 3 4 5 6 7 8 9 10; 3 4 5 6 7 8 9 10 11]%
[n,m]=size(A);
A(:,end+1:end+n-1)=0;
p=n+m-1;
id2=rem(bsxfun(@plus,p-(0:n-1)',1:p),p);
id2(~id2)=p;
id1=repmat((1:n)',1,p);
ii=sub2ind(size(A),id1,id2);
B=sum(A(ii))