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Natural number
147 (one hundred [and] forty-seven) is the natural number following 146 and preceding 148.
147 is the fourth centered icosahedral number. These are a class of figurate numbers that represent points in the shape of a regular icosahedron or alternatively points in the shape of a cuboctahedron, and are magic numbers for the face-centered cubic lattice.[1] Separately, it is also a magic number for the diamond cubic.[2]
It is also the fourth Apéry number a 3 {\displaystyle a_{3}} following 19, where[3] a n = ∑ k = 0 n ( n k ) 2 ( n + k k ) , {\displaystyle a_{n}=\sum _{k=0}^{n}{\binom {n}{k}}^{2}{\binom {n+k}{k}},}
with 147 the composite index of the nineteenth triangle number, 190.[4][5]
There are 147 different ways of representing one as a sum of unit fractions with five terms, allowing repeated fractions,[6] and 147 different self-avoiding polygonal chains of length six using horizontal and vertical segments of the integer lattice.[7]
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