{"id":"odd-subarray-count-formula","text":"Element at index `i` in an array of length `n` appears in exactly `((i+1)*(n-i)+1)//2` odd-length subarrays, derived from total subarray count `(i+1)*(n-i)` with ceiling division by 2","truth_value":"IN","source":"entries/2026/06/06/sum-of-all-odd-length-subarrays-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":["closed-form-reduction-eliminates-iteration"],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"odd-subarray-count-formula","truth_value":"IN","reason":"premise"}]}}