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

1,1

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).

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

Prog

(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

Crossrefs

Cf. A143937, A143938, A193391.

Sequence in context: A248095 A193391 A193399 * A143938 A042428 A158554

Adjacent sequences: A193390 A193391 A193392 * A193394 A193395 A193396

Keyword

nonn,easy

Author

Emeric Deutsch, Jul 25 2011

Status

approved