Hexagonal number
Type of figurate number
Hexagonal number
A hexagonal number is a figurate number. The nth hexagonal number hn is the number of distinct dots in a pattern of dots consisting of the outlines of regular hexagons with sides up to n dots, when the hexagons are overlaid so that they share one vertex. The formula for the nth hexagonal number h n = 2 n 2 − n = n ( 2 n − 1 ) = 2 n ( 2 n − 1 ) 2 . {\displaystyle h_{n}=2n^{2}-n=n(2n-1)={\frac {2n(2n-1)}{2}}.} The first few hexagonal numbers (sequence A000384 in the OEIS) are: 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378...
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