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Molecular topological indices of the path graphs P_n
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%I #19 Feb 16 2025 08:33:02

%S 0,4,16,38,74,128,204,306,438,604,808,1054,1346,1688,2084,2538,3054,

%T 3636,4288,5014,5818,6704,7676,8738,9894,11148,12504,13966,15538,

%U 17224,19028,20954,23006,25188,27504,29958,32554,35296,38188,41234,44438

%N Molecular topological indices of the path graphs P_n

%C Maximum molecular topological index for alkane trees with n vertices.

%C See page 161 of Muller et al. paper for the definition of molecular topological index.

%D W. R. Muller, K. Szymanski, J.V. Knop and N. Trinajstich, "Molecular topological index", J. Chem. Inf. Comput. Sci., vol. 30 (1990),pp. 160-163. See Table 2 on page 162 column 4.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MolecularTopologicalIndex.html">Molecular Topological Index</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PathGraph.html">Path Graph</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F a(1) = 0; a(n) = (2n^3-3n^2+13n-18)/3 - Eric W. Weisstein, Jul 10 2011.

%F G.f.: 2*x^2*(x+1)*(2-2*x+x^2)/(1-x)^4. - _Colin Barker_, Aug 07 2012

%e If n=10 then the maximum molecular topological index is 604 which is the tenth term in the sequence.

%Y Cf. A000602.

%K nonn,easy,changed

%O 1,2

%A _Parthasarathy Nambi_, Aug 25 2006