Define <code>dp[i][0]</code> as the answer for the subarray <code>[0, i]</code>.

Similarly define <code>dp[i][1]</code> as the answer for the subarray <code>[0, i]</code> if we wanted to count even-sum subsequences.

If <code>nums[i]</code> is odd, <code>dp[i][x] = 2ⁱ</code>.

Otherwise, <code>dp[i][x] = dp[i - 1][x] * 2</code>.

<code>dp[0][1] = 1</code> if <code>nums[0]</code> is odd, and 0 otherwise.

<code>dp[0][0] = 2</code> if <code>nums[0]</code> is even, and 1 otherwise (since an empty subsequence has an even sum).