A193393 - OEIS

%I #33 Sep 08 2022 08:45:58

%S 27,109,271,545,963,1557,2359,3401,4715,6333,8287,10609,13331,16485,

%T 20103,24217,28859,34061,39855,46273,53347,61109,69591,78825,88843,

%U 99677,111359,123921,137395,151813,167207,183609,201051,219565,239183,259937,281859,304981,329335,354953

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

%H Vincenzo Librandi, <a href="/A193393/b193393.txt">Table of n, a(n) for n = 1..10000</a>

%H A. A. Dobrynin, I. Gutman, S. Klavzar, P. Zigert, <a href="http://www.fmf.uni-lj.si/~klavzar/preprints/Wiener-survey.pdf">Wiener Index of Hexagonal Systems</a>, Acta Applicandae Mathematicae 72 (2002), pp. 247-294.

%H I. Gutman, S. Klavzar, M. Petkovsek, and P. Zigert, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match43/match43_49-66.pdf">On Hosoya polynomials of benzenoid graphs</a>, Comm. Math. Comp. Chem. (MATCH), 43, 2001, 49-66.

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

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

%F G.f.: x*(27 + x - 3*x^2 + 7*x^3)/(1-x)^4. - _Bruno Berselli_, Jul 27 2011

%o (Magma) [(16*n^3 + 24*n^2 + 62*n - 21)/3: n in [1..40]]; // _Vincenzo Librandi_, Jul 26 2011

%o (PARI) a(n)=(16*n^3+24*n^2+62*n)/3-7 \\ _Charles R Greathouse IV_, Jul 26 2011

%Y Cf. A143937, A143938, A193391.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, Jul 25 2011