The MokraBela Triangle: A Six-Table Extension with Column Sum Formula S₂(k) = 3k²(2k−1) and Prime Indexing Structure

Version 1.0 — English & Arabic Editions ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━THE THEOREM — النظرية━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ [English]The MokraBela Triangle is defined by:T(n, imp) = imp × (2n + imp) = (n + imp)² − n²where imp = 1, 3, 5, ..., 71 (odd column headers)and n = 1, 2, 3, ... (row index). [عربي]مثلث موقرابيلا معرَّف بـ:T(n, imp) = imp × (2n + imp) = (n + imp)² − n²حيث imp = 1,3,5,...,71 (رؤوس الأعمدة الفردية)و n = 1,2,3,... (مؤشر الصف) ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━MAIN RESULTS — النتائج الرئيسية━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ [English]1. Six tables classified by sign and type of row parameter2. Closed-form column sum: S₂(k) = 3k²(2k−1) = 6k³−3k² Verified exactly for all 36 columns (k=1 to 36)3. Prime indexing: primes appear as natural row labels in tables F3–F6, verified for all 35 prime rows4. Symmetry identity: T(n,imp) + T(−n,imp) = 2×imp²5. New integer sequence: 1, 36, 135, 336, 675, 1188, 1911... NOT FOUND in OEIS (searched March 6, 2026) Formula: a(k) = 3k²(2k−1) = 3 × A015237(k) Submitted to OEIS for registration [عربي]١. ستة جداول مصنَّفة حسب علامة ونوع معامل الصف٢. صيغة مغلقة: S₂(k) = 3k²(2k−1)، تحقق كامل لـ 36 عموداً٣. الأعداد الأولية كفهارس طبيعية في الجداول F3–F6٤. هوية التماثل: T(n,imp) + T(−n,imp) = 2×imp²٥. متتالية جديدة غير مسجلة في OEIS ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━FILES — الملفات━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ - MokraBela_Triangle_EN.pdf — Full English edition- MokraBela_Triangle_AR.pdf — النسخة العربية الكاملة ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━RELATION TO PREVIOUS WORK━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ This paper extends the MokraBela Theorem (2026):DOI: 10.5281/zenodo.18877838 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ © 2026 Mokrane Ahmed — Sidi Bel Abbès, Algeriamokranedido@gmail.com