Question

0 1 2 … n-2 n-1 1 0 1 … n-3 n-2 2 1 0 … n-4 n-3 Dn= ........

Answer 1

Dn =

rn-r(n-1),r(n-1)-r(n-2),..,r2-r1

0 1 2 .. n-2 n-1

1 -1 -1 .. -1 -1

1 1 -1 .. -1 -1

.. .. .. .. ..

1 1 1 .. -1 -1

1 1 1 .. 1 -1

c1+cn,c2+cn,..,c(n-1)+cn

n-1 n n+1 .. 2n-3 n-1

0 -2 -2 .. -2 -1

0 0 -2 .. -2 -1

.. .. .. .. ..

0 0 0 .. -2 -1

0 0 0 .. 0 -1

=(n-1)*(-1)^(n-1)*2^(n-2)