cp's OEIS Frontend

A193398 Hyper-Wiener index of a benzenoid consisting of a double-step spiral chain of n hexagons (n >= 2, s = 21; see the Gutman et al. reference).

%I A193398 #33 Sep 08 2022 08:45:58
%S A193398 215,636,1557,3018,5555,8968,14225,20790,30159,41364,56525,74146,
%T A193398 97067,123168,156105,193038,238535,288940,349829,416634,496035,582456,
%U A193398 683777,793318,920255,1056708,1213245,1380690,1571099,1773904,2002745,2245566,2517687,2805468
%N A193398 Hyper-Wiener index of a benzenoid consisting of a double-step spiral chain of n hexagons (n >= 2, s = 21; see the Gutman et al. reference).
%H A193398 Vincenzo Librandi, <a href="/A193398/b193398.txt">Table of n, a(n) for n = 2..10000</a>
%H A193398 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 A193398 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 A193398 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-6,0,6,-2,-2,1).
%F A193398 a(n) = (6*n^4 + 48*n^3 + 146*n^2 - 316*n + 439 + (-1)^n*(6*n^2 + 24*n - 83))/4.
%F A193398 G.f.: x^2*(215 + 206*x - 145*x^2 - 78*x^3 + 221*x^4 - 126*x^5 - 99*x^6 + 94*x^7)/((1+x)^3*(1-x)^5). - _Bruno Berselli_, Jul 26 2011
%p A193398 a := n -> (3/2)*n^4+12*n^3+(3/2)*n^2*(-1)^n+(73/2)*n^2+6*n*(-1)^n-79*n+(83/4)*(-1)^(n+1)+439/4: seq(a(n), n = 2 .. 35);
%t A193398 LinearRecurrence[{2,2,-6,0,6,-2,-2,1},{215,636,1557,3018,5555,8968,14225,20790},40] (* _Harvey P. Dale_, Aug 30 2017 *)
%o A193398 (Magma) [(3/2)*n^4+12*n^3+(3/2)*n^2*(-1)^n+(73/2)*n^2+6*n*(-1)^n-79*n+(83/4)*(-1)^(n+1)+439/4: n in [2..40]]; // _Vincenzo Librandi_, Jul 26 2011
%o A193398 (PARI) a(n)=(6*n^4+48*n^3+146*n^2-316*n+439+(-1)^n*(6*n^2+24*n-83))/4 \\ _Charles R Greathouse IV_, Jul 28 2011
%Y A193398 Cf. A143937, A143938, A193391, A193392, A193393, A193394, A193395, A193396, A193397.
%K A193398 nonn,easy
%O A193398 2,1
%A A193398 _Emeric Deutsch_, Jul 25 2011