A193391 Wiener index of a benzenoid consisting of a spiral chain of n hexagons (s=1; see the Gutman et al. reference).

27, 109, 271, 529, 899, 1397, 2039, 2841, 3819, 4989, 6367, 7969, 9811, 11909, 14279, 16937, 19899, 23181, 26799, 30769, 35107, 39829, 44951, 50489, 56459, 62877, 69759, 77121, 84979, 93349, 102247, 111689, 121691, 132269, 143439, 155217, 167619, 180661, 194359

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) = (27 - 26*n + 72*n^2 + 8*n^3)/3.

G.f.: x*(27 + x - 3*x^2 - 9*x^3)/(1-x)^4. - Bruno Berselli, Jul 27 2011

Mathematica

A193391[n_] := 2*n*(4*n*(n + 9) - 13)/3 + 9; Array[A193391, 50] (* Paolo Xausa, May 08 2026 *)

Prog

(Magma) [(27 - 26*n + 72*n^2 +8*n^3)/3: n in [1..30]]; // Vincenzo Librandi, Jul 26 2011
(PARI) a(n)=(8*n^3+72*n^2-26*n)/3+9 \\ Charles R Greathouse IV, Jul 26 2011

Crossrefs

Cf. A143937, A143938, A193392.

Sequence in context: A042426 A042424 A248095 * A193399 A193393 A143938

Adjacent sequences: A193388 A193389 A193390 * A193392 A193393 A193394

Keyword

nonn,easy

Author

Emeric Deutsch, Jul 25 2011

Status

approved