A121318 Molecular topological indices of the path graphs P_n.

0, 4, 16, 38, 74, 128, 204, 306, 438, 604, 808, 1054, 1346, 1688, 2084, 2538, 3054, 3636, 4288, 5014, 5818, 6704, 7676, 8738, 9894, 11148, 12504, 13966, 15538, 17224, 19028, 20954, 23006, 25188, 27504, 29958, 32554, 35296, 38188, 41234, 44438

Offset: 1

Author

Parthasarathy Nambi, Aug 25 2006

Keywords

• nonn
• easy

Comments

Maximum molecular topological index for alkane trees with n vertices.

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

Examples

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

Links

• W. R. Müller, 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.
• Eric Weisstein's World of Mathematics, Molecular Topological Index
• Eric Weisstein's World of Mathematics, Path Graph
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000602.

Formula

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

G.f.: 2*x^2*(x+1)*(2-2*x+x^2)/(1-x)^4. - Colin Barker, Aug 07 2012