Deterministic pushdown automata for the language $L=\{ a^ib^j| i \neq 2j+1, i,j>0\}$ where $\Sigma = \{a,b\}$
Yes, here the idea of one with three states. I don't know stuff formally enough to write tuples.

Keep track of the parity of 'a's you read in two states.
If you read 'aa', push A on the stack
When you hit b, you better be on odd parity
Pop 'A' for every 'b' you read
At the end of the input, succeed if the stack is exactly empty.

This accepts only when i == 2j+1. Then, invert the last step, while keeping the requirement to keep it in the format $\{a^ib^j\}$ to get the version below. This requires adding one more state.
This might be a valid formal version, or it might not:
state,      input (z=end-of-string),
               top of stack (E=empty, *=anything),
                  action
q_a_even,   a, *, do nothing and transition to q_a_odd
q_a_even,   b, *, transition to q_b_ok
q_a_even,   z, *, succeed
q_a_odd,    a, *, push 'A' and transition to q_a_even
q_a_odd,    b, E, transition to q_b_ok
q_a_odd,    b, A, pop and transition to q_b_danger
q_a_odd,    z, *, succeed
q_b_danger, a, *, fail
q_b_danger, b, E, succeed
q_b_danger, b, A, pop and transition to q_b_danger
q_b_danger, z, A, succeed
q_b_danger, z, E, fail
q_b_ok,     a, *, fail
q_b_ok,     b, *, transition to q_b_ok
q_b_ok,     z, *, succeed