Definition D46 The pentagonal numbers PnP_nPn, n≥0n \geq 0n≥0, are defined as Pn=1+4+7+⋯+(3n−2)=∑k=1n(3k−2) .P_n = 1 + 4 + 7 + \cdots + (3 n - 2) = \sum_{k=1}^n (3 k - 2) \;. Pn=1+4+7+⋯+(3n−2)=k=1∑n(3k−2).