Explicit Square Constructions for Odd-Length Geometric Progressions

OEIS A092960 records the least square representable as one plus the sum of n successive terms of a geometric progression, with value $0$ when no such square exists. For every odd n≥3, we give an explicit n-term geometric progression with first term 2ⁿ-3 and common ratio $2$ whose sum plus $1$ equals (2ⁿ-2)². This is an unconditional existence theorem for that explicit class of progressions. When applied to A092960 under the natural interpretation that such positive-integer ratio-$2$ progressions are admissible and that $0$ is used only as the nonexistence fallback, it gives the upper bound\[a(n)≤(2^n-2)^2\]at every odd index. The argument concerns existence and an upper bound, not an exact formula for the odd-index minima.