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A245833
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The Szeged index of the triangle-shaped benzenoid T_k (see Fig. 5.7 of the Diudea et al. reference).
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0
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54, 540, 2610, 8820, 23940, 55944, 117180, 225720, 406890, 694980, 1135134, 1785420, 2719080, 4026960, 5820120, 8232624, 11424510, 15584940, 20935530, 27733860, 36277164, 46906200, 60009300, 76026600, 95454450, 118850004, 146835990, 180105660
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OFFSET
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1,1
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REFERENCES
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M. V. Diudea, I. Gutman, J. Lorentz, Molecular Topology, Nova Science Publishers, Huntington, NY (2001).
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LINKS
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FORMULA
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a(k) = (k^6+12k^5+49k^4+84k^3+58k^2+12k)/4.
G.f.: 18z(3+9z-2z^2)/(1-z)^7.
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EXAMPLE
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a(1)=54; indeed, the benzenoid consists of 1 hexagon and each of its six edges contributes 3*3 towards the Szeged index; 6*9 = 54.
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MAPLE
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a := proc (n) options operator, arrow: (1/4)*n^6+3*n^5+(49/4)*n^4+21*n^3+(29/2)*n^2+3*n end proc: seq(a(n), n = 1 .. 30);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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