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Table 25 Magic topological formulas for clusters, continued

From: Magic Mathematical Relationships for Nanoclusters

fcc tetrahedron  
 Wiener \(\frac {1}{168}n^{7} + \frac {1}{12}n^{6} + \frac {7}{15}n^{5} + \frac {4}{3}n^{4} + \frac {49}{24}n^{3}+\frac {19}{12}n^{2}+\frac {17}{35}n\)
 Reverse Wiener \(\frac {1}{126}n^{7} + \frac {1}{12}n^{6} + \frac {61}{180}n^{5} + \frac {7}{12}n^{4} +\frac {5}{36}n^{3}-\frac {2}{3}n^{2}-\frac {17}{35}n\)
 HyperWiener \(\frac {1}{672}n^{8}+\frac {3}{112}n^{7} + \frac {47}{240}n^{6} + \frac {3}{4}n^{5} + \frac {155}{96}n^{4} + \frac {31}{16}n^{3}+\frac {499}{420}n^{2}+\frac {2}{7}n\)
 Szeged \(\frac {71}{60480}n^{9}+\frac {71}{3360}n^{8} + \frac {227}{1440}n^{7}+\frac {151}{240}n^{6} + \frac {4163}{2880}n^{5} + \frac {917}{480}n^{4} + \frac {20599}{15120}n^{3}+\frac {123}{280}n^{2}+\frac {1}{30}n\)
bcc tetrahedron  
 Wiener \(\frac {1}{21}n^{7} + \frac {1}{2}n^{6} + \frac {21}{10}n^{5} + \frac {9}{2}n^{4} + \frac {31}{6}n^{3}+3n^{2}+\frac {24}{35}n\)
 Reverse Wiener \(\frac {4}{63}n^{7} + \frac {1}{2}n^{6} + \frac {287}{180}n^{5} + \frac {7}{3}n^{4} + \frac {37}{36}n^{3}-\frac {5}{6}n^{2}-\frac {24}{35}n\)
 HyperWiener \(\frac {1}{42}n^{8}+\frac {13}{42}n^{7} + \frac {587}{360}n^{6} + \frac {179}{40}n^{5} + \frac {493}{72}n^{4} + \frac {139}{24}n^{3}+\frac {787}{315}n^{2}+\frac {89}{210}n\)
 Szeged \(\frac {1}{81}n^{9}+\frac {1}{6}n^{8} + \frac {176}{189}n^{7}+\frac {25}{9}n^{6} + \frac {641}{135}n^{5} + \frac {83}{18}n^{4} + \frac {188}{81}n^{3}+\frac {4}{9}n^{2}-\frac {4}{315}n\)
Diamond cubic  
 Wiener \(\frac {7648}{105}n^{7} + \frac {1912}{15}n^{6} + \frac {1792}{15}n^{5} - \frac {40}{3}n^{4} - \frac {374}{15}n^{3}-\frac {902}{15}n^{2}-\frac {48}{35}n+12\)
 Reverse Wiener \(\frac {12512}{105}n^{7} + \frac {1448}{15}n^{6} + \frac {548}{15}n^{5} - \frac {392}{3}n^{4} - \frac {811}{15}n^{3}+\frac {452}{15}n^{2}+\frac {2043}{35}n-24\)
 HyperWiener \(\frac {472}{5}n^{8}+\frac {23648}{105}n^{7} + \frac {3976}{15}n^{6} + \frac {842}{15}n^{5} - \frac {926}{15}n^{4} - \frac {1219}{15}n^{3}-\frac {971}{15}n^{2}+\frac {312}{35}n+18\)
 Szeged \(\frac {512}{3}n^{9}+\frac {5896}{21}n^{8} + 208n^{7}-\frac {1504}{5}n^{6} +\frac {503}{5}n^{5} - 1n^{4} + 193n^{3}-\frac {4721}{105}n^{2}-\frac {574}{15}n+24\)