A193393 Wiener index of a benzenoid consisting of a zig-zag chain of n hexagons (s=13; see the Gutman et al. reference).

27, 109, 271, 545, 963, 1557, 2359, 3401, 4715, 6333, 8287, 10609, 13331, 16485, 20103, 24217, 28859, 34061, 39855, 46273, 53347, 61109, 69591, 78825, 88843, 99677, 111359, 123921, 137395, 151813, 167207, 183609, 201051, 219565, 239183, 259937, 281859, 304981, 329335, 354953

Offset: 1

Author

Emeric Deutsch, Jul 25 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• A. A. Dobrynin, I. Gutman, S. Klavzar, P. Zigert, Wiener Index of Hexagonal Systems, Acta Applicandae Mathematicae 72 (2002), pp. 247-294.
• I. Gutman, S. Klavzar, M. Petkovsek, and P. Zigert, On Hosoya polynomials of benzenoid graphs, Comm. Math. Comp. Chem. (MATCH), 43, 2001, 49-66.
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A143937, A143938, A193391.

Programs

Magma

[(16*n^3 + 24*n^2 + 62*n - 21)/3: n in [1..40]]; // Vincenzo Librandi, Jul 26 2011

PARI

a(n)=(16*n^3+24*n^2+62*n)/3-7 \\ Charles R Greathouse IV, Jul 26 2011

Formula

a(n) = (16*n^3 + 24*n^2 + 62*n - 21)/3.

G.f.: x*(27 + x - 3*x^2 + 7*x^3)/(1-x)^4. - Bruno Berselli, Jul 27 2011